Question

Assuming that a year consists of $365$ days, the probability that a group of $n$ people $(n\le 365)$ have all different birthdays is

• A. $\frac{365}{{365}^n}$
• B. $\frac{n}{{365}^n}$
• C. $\frac{{}^{365}{P}_n}{{365}^n}$
• D. $\frac{{}^n{P}_n}{{365}^n}$

Answer 1

Answer: (C)

$\frac{{}^{365}{P}_n}{{365}^n}$

The $n$ birthdays can be selected and ordered in ${}^{365}{P}_n$ ways.
Hence, probability $=\frac{{}^{365}{P}_n}{{365}^n}$