Short Descriptions and equations of how problems can be solv

Short Descriptions and equations of how problems can be solved are greatly appreciated.

5 The Birthday Problem consider the birthdays of the students in a class of size k (k

Solution

a) There are 365^k possible outcomes, as each student has 365 possible birthdays.

b) In this case, there are P(365,k) possible outcomes, as it matters as to which one has the birthday.

In factorial notation,

#ways = 365! / (365 - k)! [ANSWER]

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c) From parts A and B,

P(distinct birthday) = [365! / (365 - k)!] / 365^k

P(distinct birthday) = 365! / [(365 - k)! 365^k] [ANSWER]

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Note that

P(at least two) = 1 - P(all distinct)

Thus,

P(at least two) = 1 - 365! / [(365 - k)! 365^k] [answer]