Combination question - Bridge hands containing 3 aces or 7 diamonds or both?

How many bridge hands contain exactly 3 aces or exactly seven diamonds or both? One answer is: 4C3 * 48C10 + 13C7 * 39C6 - (12C7 * 3C3 * 36C3 + 1C1 * 12C6 * 3C2 * 36C4) I know it is the inclusion - exclusion principle. I don't understand the calculation inside the brackets. hope someone could post an... show more How many bridge hands contain exactly 3 aces or exactly seven diamonds or both?
One answer is:

4C3 * 48C10 + 13C7 * 39C6 - (12C7 * 3C3 * 36C3 + 1C1 * 12C6 * 3C2 * 36C4)

I know it is the inclusion - exclusion principle. I don't understand the calculation inside the brackets.
hope someone could post an explanation. Thanks.
1 answer 1