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In a group of 9 people, what is the probability that they all have different birthdays?...

In a group of 9 people, what is the probability that they all have different birthdays? [Assume that each is equally likely to be born on any of the 365 days of the year, i.e. no one is born on Feb. 29 in a leap year.]

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Answer #1

All 9 people have different birthdays means,

first person have birthday in any of 365 days

second person can have birthday of any of 364 days only (because he cannot share his birthday with first person)

third person can have birthday of any of 363 days only (because he cannot share his birthday with first two person)

and so on

So probability that all 9 people have different birthdays is:

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