- #1
davedave
- 50
- 0
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.