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## Homework Statement

4 cards are dealt from a 52-card deck. How many hands contain 2 distinct pairs?

## Homework Equations

This is an expression I come up with 13C1x4C2x12C1x4C2.

## The Attempt at a Solution

This is how I approach it.

From the 13 ranks, I choose 1.

In this rank, I choose 2 cards from 4.

From the remaining 12 ranks, I choose 1.

In this rank, I choose 2 cards from 4.

Now, I do the following calculations with combinations.

13C1x4C2x12C1x4C2 = 5616.

My neighbor told me that it's wrong. He didn't explain why it was wrong. I cannot find any mistakes.

Please explain what I have done wrong. Thank you very much.