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There are 50 students in class what is the probability that 2 of them have the...

There are 50 students in class what is the probability that 2 of them have the same birthday? (Use combination)

Math   Statistics-And-Probability   
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Answer #1

There are 365 days in a year. Since each person can have birthday in 365 ways so number of ways 50 people can select their birthday is

Number of ways of choosing 2 students out of 50 to have same birthday is C(50,2).

We need to find the probability that two students have same birthday. Two students can have their birthday in one of the 365 days. That is number of ways they can chose their birthday is C(365, 1).

Rest 50 -2 = 48 students need to chose their birthday out of remaining 365 -1 = 364 days such that each have different birthday. That is they can chose their birthday is C(364, 48) ways.

So total number of ways they can chose their birthday such that two of them have the same birthday is

C(50,2) * C(365, 1) * C(364, 48)

The probability that 2 of them have the same birthday is

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