Fifty-four distinct birthdays

Topic: Random experiments and probability · more questions on this topic
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Fifty-four people are in a room. Birthdays are independent and uniformly distributed over 365 days. What is the probability that no two share a birthday? A numerical value to three decimal places is enough, together with the exact product it approximates.

Worked answer (click to show)

\mathbb{P}(\text{all different})=\frac{365\times 364\times\cdots\times 312}{365^{54}}\approx 0.016.