Question

Birthday Problem In how many ways can 2 people each have different birthdays? Assume that there are 365 days in a year.

Short answer

The required number of ways is 132860.

Step-by-step solution

Step 1. Given information.

Number of days in a year is 365.

Number of people is 2 and they have different birthdays.

Step 2. Determine the number of ways.

This is an example of a permutation without repetition.

• The number of choices for the first person's birthday is 365.
• The number of choices for the second person's birthday is 364 because both people have different birthdays.

By the Multiplication Principle, we get

$365\times 364=132860$

Step 3. Conclusion.

The required number of ways is 132860.