Question

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

Short answer

The required number of ways is 6302555018760.

Step-by-step solution

Step 1. Given information.

Number of days in a year is 365.

Number of people is 5 and they have different birthdays.

Step 2. Determine the number of ways.

This is an example of a permutation without repetition in which 5 days are chosen from 365 distinct days.

$\begin{array}{rcl}P(365,5)& =& \frac{365!}{(365-5)!}\\ & =& \frac{365!}{360!}\\ & =& \frac{365·364·363·362·361·360!}{360!}\\ & =& 6302555018760\end{array}$

Step 3. Conclusion.

The required number of ways is 6302555018760.