Birthday problem
Probability
Level
3
There are 20 people in a room. Find the probability that all of them have different birthdays?
The answer is 0.5885616.
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1 solution
There are 2 0 people thus possible combinations for their birthday are 3 6 5 2 0 And the possible permutations for their different birthday are 3 6 5 ! ÷ ( 3 6 5 − 2 0 ) ! . Thus the probability that all are having different birthday is 3 6 5 2 0 3 6 5 ! ÷ ( 3 6 5 − 2 0 ) ! = 0 . 5 8 8 5 6 1 6 . . . and thus the answer is 0 . 5 8 9