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