Question

Assuming that a year consits of 365 days, the probability that a group of 30 people have all different birthdays is

• A. $\frac{365}{{365}^{30}}$
• B. $\frac{30}{{365}^{30}}$
• C. $\frac{{}^{365}{P}_{30}}{{365}^{30}}$
• D. $\frac{{}^{30}{P}_{30}}{{365}^{30}}$

Answer 1

Answer: (C)

$\frac{{}^{365}{P}_{30}}{{365}^{30}}$

The each person has $365$ days as options for his birthday
$n\left(S\right)={365}^{30}$
For unique birthdays, choose any $30$ days and assign each person each day
$n\left(E\right)=P(365,30)$
$P=\frac{{}^{365}{C}_{30}}{{365}^{30}}$