Pierre works five days a week. He has 12 shirts, 8 pants, 8 ties, and 4...

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Pierre works five days a week. He has 12 shirts, 8 pants, 8ties, and 4 jackets that he can wear to work. Of these, 4 shirts, 3pants, 2 ties, and 2 jackets are blue. Each day he randomly selectsone of each item to wear. Assume the selections are independent,and assume his butler launders the clothes every night so he hasfull closet each morning.
What is the probability pierres entire outfit next Monday willbe blue?
What is the probability that Pierre will wear entirely blueoutfits on Monday and Friday while wearing outfits which are notentirely blue on Tuesday through Thursday.
What is the probability that Pierre will wear entirely blueoutfits on Monday through Friday while wearing outfits which arenot entirely blue on Tuesday through Thursday?
What is probability Pierre will wear an entirely blue outfit onexactly 2 of the 5 days next week?
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1We need to find the probability of pierre choosing every piece of clothing which is blue under the assumption that his choices are independent therefore he can select a blue shirt from among 12 shirts out of which 4 are bluein shirt C412 or C124 ways he can select pantstiesjacket respectively in pants C83 ways ties C82 ways jacket C42 ways Since his selection of each piece of clothing is independent of each otherwe can multiply these results to get the probability of choosing a blue See Answer

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