Probability and statistics

Question

(a) There are 17 appetizers avallable at a restaurant. From these, Torn is to choose 13 for his party.

How many groups of 13 appetizers are possible?

(b) A certain committee consists of 18 people. From the committee, a president, a vice-president, a secretary, and a treasurer are to be chosen. in how many ways can these 4 offices be filled? Assume that a committee member can hold at most one of these offices?

Answer 1

a

17C13 = 17! /(13!4!) = 2380

b

18P4 = 18! / (18-4)! = 73440

Answer 2

These are fundamental problems

a) This is 17 choose 13 or ₁₇C₃ = 17!/(3!14!)

b) This is 18 choose 4 where order matters ₁₈P₄ = 18!/14!

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