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I understand the answer to be 12 choose 2 * 12 choose 2 over 24 choose 4.

I don't really understand why, or what principle I can extract from the problem. I can understand that we are putting the total possible outcomes in the denominator, but not how the numerator represents the exact 2 by 2 requirement the problem states

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    You're choosing $2$ out of $12$ twice. $2\cdot {{12}\choose{2}}$2012-08-06

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