Chapter 13.2, Problem 48AYU

Birthday Problem In how many ways can 5 people all have different birthdays? Assume that there are 365 days in a year.

To determine

To find: In how many ways can 5 people each have different birthdays? Assume that there are 365 days in a year.

Answer to Problem 48AYU

6302555018760

Explanation of Solution

Given:

5 people each have different birthdays. Assume that there are 365 days in a year.

Formula used:

$P\left(n,r\right)=\frac{n!}{\left(n-r\right)!}$

Calculation:

Assuming that there are 365 days in a year.

Number of choices for first person is 365 days.

Number of choices for second person is remaining 364 days.

Number of choices for third person is remaining 363 days.

Number of choices for fourth person is remaining 362 days.

Number of choices for fifth person is remaining 361 days.

In other words, the number of ways is given by $P\left(365,5\right)=\frac{365*364*363*362*361*360!}{\left(365-5\right)!}$.

Hence, total number of choices is $365*364*363*362*361=6302555018760$.