Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Suppose there are 4 people and each person has an associated birth month. How many ways are there so that at least 2 people share the same birth month?

My first instinct is that it's $12\cdot12\cdot11\cdot10$ but that doesn't seem right.

share|improve this question
add comment

1 Answer 1

$$(\text{The number of ways at least 2 people share the same birth month}) =$$ $$(\text{The number of all possible arrangements of birth months})-$$ $$(\text{The number of ways no 2 people share the same birth month})$$ $$=(12\times12\times12\times 12)-(12\times 11\times 10\times 9)=20736-11880=8856$$

share|improve this answer
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.