Need some help with some combinatorics problem! We are supposed to use the Inclusion-Exclusion principle to solve: "how many bridge hands contain exactly 3 clubs, or exactly 5 diamonds or exactly 3 aces?"
I know you do something like: 
|3 clubs|+|3aces|+|5dimonds| - |3clubs AND 3 aces| - |3clubs AND 5 diamonds| -...... +|all 3 intersected| 
But I'm really struggling with find the cases where the aces may or may not be a club/diamond.