Question
1. How many permutations are there of the letters in the word "CATS" taken three at a time
2. A pizza parlor offers five toppings on its pizza. How many different pizzas are there with two, three or four toppings?
3. An urn contains four red balls and six white balls. A sample of four balls is selected.
(a) How many samples are possible?
(b) How many samples contain exactly three white balls?
(c) How many samples contain four white balls?
4. Joe goes to a mexican restaurant and order nachos. He can have just cheese or add any of the following: chicken, onion, sour cream or olives. How many different variations of nachos are possible?
5. Using the Binomial theorem expand the expression: (x + 5y)⁵
6. Let S = {a, b, c, d, e} be a sample space, E = {a, b, e}, and F = {b, c}.
(a) Determine the events E ∪ F and E ∩ F.
(b) Are E ∪ F and E ∩ F mutually exclusive?
7. A fair coin is tossed six times. What is the probability of obtaining at most five heads?
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        • 18. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
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        1.26mstwenty4_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
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        1.05mstwenty4_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
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        900μstwenty4_siteHomeworkLibrary.php#201
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        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
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        Backtrace
        • 14. app/Repositories/HomeworkLibraryRepository.php:30
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      • select * from `subjects` where `subjects`.`id` in (60)
        1.05mstwenty4_siteHomeworkLibraryRepository.php#30
        Backtrace
        • 19. app/Repositories/HomeworkLibraryRepository.php:30
        • 20. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
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        • 23. app/Repositories/HomeworkLibraryRepository.php:39
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      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` = 55054 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'question' order by `order` asc, `id` asc
        1.14mstwenty4_siteHomeworkLibrary.php#260
        Bindings
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        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
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        Backtrace
        • 15. app/Models/HomeworkLibrary/HomeworkLibrary.php:260
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        • 19. vendor/league/fractal/src/TransformerAbstract.php:128
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        Backtrace
        • 15. app/Models/HomeworkLibrary/HomeworkLibrary.php:260
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