You have books on your shelf. You notice that of them are written b...

Question
You have books on your shelf. You notice that of them are written by one author , and of them are written by another author. If you choose books from your shelf at random, what is the probability that will be by one author and will be by another author ?
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We choose 3 books out of seven and we do it this way
7C3= 7*6
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      • Illuminate\Cache\Events\CacheHit (175μs)
      • Illuminate\Cache\Events\CacheHit (180μs)
      • Illuminate\Cache\Events\CacheHit (444μs)
      • creating: site.layouts.app (621μs)
      • composing: site.layouts.app (30μs)
      • creating: components.canonical (789μs)
      • composing: components.canonical (104μs)
      • creating: components.open-graph (214μs)
      • composing: components.open-graph (76μs)
      • creating: site.headers.header (351μs)
      • composing: site.headers.header (82μs)
      • Illuminate\Cache\Events\CacheHit (2.03ms)
      • creating: components.footer (154μs)
      • composing: components.footer (97μs)
      • Illuminate\Cache\Events\CacheHit (1.02ms)
      • Illuminate\Cache\Events\CacheMissed (525μs)
      • Illuminate\Database\Events\StatementPrepared (7.12ms)
      • Illuminate\Database\Events\QueryExecuted (1.33ms)
      • eloquent.retrieved: App\Models\SubjectCat (80μs)
      • Illuminate\Cache\Events\KeyWritten (1.98ms)
      • Illuminate\Cache\Events\CacheHit (754μs)
      • Illuminate\Cache\Events\CacheHit (219μs)
      • Illuminate\Cache\Events\CacheHit (560μs)
      • Illuminate\Cache\Events\CacheHit (222μs)
      • Illuminate\Cache\Events\CacheHit (522μs)
      • Illuminate\Cache\Events\CacheHit (329μs)
      • Illuminate\Cache\Events\CacheHit (506μs)
      • Illuminate\Cache\Events\CacheHit (270μs)
      • Illuminate\Cache\Events\CacheHit (194μs)
      • Illuminate\Cache\Events\CacheHit (189μs)
      • Illuminate\Cache\Events\CacheHit (210μs)
      • Illuminate\Cache\Events\CacheHit (207μs)
      • creating: components.forms.contact-us (336μs)
      • composing: components.forms.contact-us (156μs)
      • creating: components.forms.get-started (128μs)
      • composing: components.forms.get-started (67μs)
      • creating: components.forms.free-tool-download (265μs)
      • composing: components.forms.free-tool-download (73μs)
      • creating: components.forms.claim-free-worksheet (144μs)
      • composing: components.forms.claim-free-worksheet (66μs)
      • creating: components.forms.tutor-subscription-waitlist (192μs)
      • composing: components.forms.tutor-subscription-waitlist (72μs)
      • creating: components.forms.tutor-subscription-join (103μs)
      • composing: components.forms.tutor-subscription-join (63μs)
      • creating: components.forms.tutor-support (175μs)
      • composing: components.forms.tutor-support (68μs)
      • 311 x Illuminate\Cache\Events\CacheHit (17.99%)
        133ms
        20 x Illuminate\Database\Events\StatementPrepared (16.82%)
        125ms
        20 x Illuminate\Database\Events\QueryExecuted (13.3%)
        98.61ms
        11 x Illuminate\Cache\Events\CacheMissed (1.71%)
        12.69ms
        11 x Illuminate\Cache\Events\KeyWritten (1.45%)
        10.76ms
        1 x Illuminate\Foundation\Events\LocaleUpdated (0.81%)
        6.03ms
        1 x Illuminate\Routing\Events\Routing (0.26%)
        1.96ms
        1 x Illuminate\Database\Events\ConnectionEstablished (0.22%)
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        1.45ms
        1 x creating: homework.show (0.15%)
        1.14ms
        1 x Illuminate\Routing\Events\RouteMatched (0.12%)
        926μs
        1 x creating: components.canonical (0.11%)
        789μs
        1 x eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.1%)
        730μs
        1 x creating: site.layouts.app (0.08%)
        621μs
        2 x eloquent.retrieved: App\Models\Subject (0.08%)
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        1 x eloquent.booting: App\Models\SubjectCat (0.07%)
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        214μs
        1 x creating: components.forms.tutor-subscription-waitlist (0.03%)
        192μs
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        175μs
        1 x composing: components.breadcrumbs (0.02%)
        173μs
        1 x composing: components.forms.contact-us (0.02%)
        156μs
        1 x creating: components.footer (0.02%)
        154μs
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        144μs
        1 x creating: components.forms.get-started (0.02%)
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        104μs
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        103μs
        1 x composing: components.footer (0.01%)
        97μs
        1 x eloquent.booted: App\Models\SubjectCat (0.01%)
        84μs
        1 x composing: site.headers.header (0.01%)
        82μs
        1 x composing: components.open-graph (0.01%)
        76μs
        1 x composing: components.forms.free-tool-download (0.01%)
        73μs
        1 x composing: components.forms.tutor-subscription-waitlist (0.01%)
        72μs
        1 x eloquent.booted: App\Models\Subject (0.01%)
        68μs
        1 x composing: components.forms.tutor-support (0.01%)
        68μs
        1 x composing: components.forms.get-started (0.01%)
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        1 x composing: components.forms.claim-free-worksheet (0.01%)
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        1 x composing: components.forms.tutor-subscription-join (0.01%)
        63μs
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      • 1x homework.showshow.blade.phpblade
      • 1x components.breadcrumbsbreadcrumbs.blade.phpblade
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      • 1x components.open-graphopen-graph.blade.phpblade
      • 1x site.headers.headerheader.blade.phpblade
      • 1x components.footerfooter.blade.phpblade
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      • 1x components.forms.get-startedget-started.blade.phpblade
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      • 1x components.forms.tutor-subscription-waitlisttutor-subscription-waitlist.blade.phpblade
      • 1x components.forms.tutor-subscription-jointutor-subscription-join.blade.phpblade
      • 1x components.forms.tutor-supporttutor-support.blade.phpblade
      uri
      GET college-homework-library/{category}/{subject}/{id}
      middleware
      web, utm.parameters
      controller
      App\Http\Controllers\HomeworkLibraryController@show
      namespace
      where
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      app/Http/Controllers/HomeworkLibraryController.php:79-176
      20 statements were executed, 5 of which were duplicates, 15 unique. Show only duplicated195ms
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        Backtrace
        • 13. app/Http/Controllers/HomeworkLibraryController.php:91
        • 14. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 15. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 16. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 17. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
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        28.03mstwenty4_siteHomeworkLibraryController.php#97
        Bindings
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        Backtrace
        • 16. app/Http/Controllers/HomeworkLibraryController.php:97
        • 17. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 18. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 19. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 20. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `subjects` where `subjects`.`id` in (3)
        4.1mstwenty4_siteHomeworkLibraryController.php#97
        Backtrace
        • 21. app/Http/Controllers/HomeworkLibraryController.php:97
        • 22. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 23. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 24. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 25. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
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        17.27mstwenty4_siteHomeworkLibraryController.php#97
        Backtrace
        • 21. app/Http/Controllers/HomeworkLibraryController.php:97
        • 22. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 23. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 24. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 25. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
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        11.26mstwenty4_siteHomeworkLibrary.php#201
        Bindings
        • 0: 1
        Backtrace
        • 20. app/Models/HomeworkLibrary/HomeworkLibrary.php:201
        • 26. app/Http/Controllers/HomeworkLibraryController.php:105
        • 27. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 28. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 29. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
      • select * from `solutionslibrary` where `id` <> 39994 and `subject` = 3 and `status` = 'published' and `price` > 0 order by RAND() limit 6
        11.89mstwenty4_siteHomeworkLibraryRepository.php#30
        Bindings
        • 0: 39994
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        • 2: published
        • 3: 0
        Backtrace
        • 14. app/Repositories/HomeworkLibraryRepository.php:30
        • 15. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 16. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 18. app/Repositories/HomeworkLibraryRepository.php:39
        • 19. app/Http/Controllers/HomeworkLibraryController.php:139
      • select * from `subjects` where `subjects`.`id` in (3)
        6.9mstwenty4_siteHomeworkLibraryRepository.php#30
        Backtrace
        • 19. app/Repositories/HomeworkLibraryRepository.php:30
        • 20. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 21. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 23. app/Repositories/HomeworkLibraryRepository.php:39
        • 24. app/Http/Controllers/HomeworkLibraryController.php:139
      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` = 39994 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'question' order by `order` asc, `id` asc
        19.85mstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 39994
        • 1: question
        Backtrace
        • 15. app/Models/HomeworkLibrary/HomeworkLibrary.php:260
        • 16. app/Transformers/HomeworkLibrary/HomeworkLibraryTransformer.php:58
        • 19. vendor/league/fractal/src/TransformerAbstract.php:128
        • 20. vendor/league/fractal/src/TransformerAbstract.php:107
        • 21. vendor/league/fractal/src/Scope.php:383
      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` = 39994 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'teaser' order by `order` asc, `id` asc
        4.39mstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 39994
        • 1: teaser
        Backtrace
        • 15. app/Models/HomeworkLibrary/HomeworkLibrary.php:260
        • 16. app/Transformers/HomeworkLibrary/HomeworkLibraryTransformer.php:69
        • 19. vendor/league/fractal/src/TransformerAbstract.php:128
        • 20. vendor/league/fractal/src/TransformerAbstract.php:107
        • 21. vendor/league/fractal/src/Scope.php:383
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        2.02mstwenty4_siteHomeworkLibrary.php#260
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        Backtrace
        • 15. app/Models/HomeworkLibrary/HomeworkLibrary.php:260
        • 16. app/Transformers/HomeworkLibrary/HomeworkLibraryTransformer.php:80
        • 19. vendor/league/fractal/src/TransformerAbstract.php:128
        • 20. vendor/league/fractal/src/TransformerAbstract.php:107
        • 21. vendor/league/fractal/src/Scope.php:383
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        2.08mstwenty4_siteHomeworkLibrary.php#201
        Bindings
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        Backtrace
        • 20. app/Models/HomeworkLibrary/HomeworkLibrary.php:201
        • 32. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 33. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 34. vendor/livewire/livewire/src/ComponentConcerns/RendersLivewireComponents.php:69
        • 35. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
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        3.3mstwenty4_siteSubject.php#100
        Bindings
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        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 3 limit 1
        13.55mstwenty4_siteSubject.php#100
        Bindings
        • 0: 3
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 4 limit 1
        2.76mstwenty4_siteSubject.php#100
        Bindings
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        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 10 limit 1
        8.54mstwenty4_siteSubject.php#100
        Bindings
        • 0: 10
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 33 limit 1
        1.25mstwenty4_siteSubject.php#100
        Bindings
        • 0: 33
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 11 limit 1
        14.82mstwenty4_siteSubject.php#100
        Bindings
        • 0: 11
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 5 limit 1
        1.34mstwenty4_siteSubject.php#100
        Bindings
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        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 34 limit 1
        4.68mstwenty4_siteSubject.php#100
        Bindings
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        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 31 limit 1
        28.78mstwenty4_siteSubject.php#100
        Bindings
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        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 36 limit 1
        7.72mstwenty4_siteSubject.php#100
        Bindings
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        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 28. view::components.footer:170
      App\Models\SubjectCat
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      App\Models\HomeworkLibrary\HomeworkLibrary
      7HomeworkLibrary.php
      App\Models\Subject
      2Subject.php
      App\Models\HomeworkLibrary\HomeworkLibraryFile
      2HomeworkLibraryFile.php
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