# 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...
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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.

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.

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