# Probability involving equal sets of 26 cards from a deck of 52

• Sep 28th 2010, 07:56 PM
Zennie
Probability involving equal sets of 26 cards from a deck of 52
An ordinary deck of cards is divided into two equal sets randomly. What is the probability that each set contains exactly 13 red cards?

I am having trouble even being sure where to begin on this problem. Can someone help me through the steps. I know how to find the number of total possible sets of 26 cards, i.e. 52 choose 26. But I don't know what to do after that.
• Sep 28th 2010, 08:29 PM
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Quote:

Originally Posted by Zennie
An ordinary deck of cards is divided into two equal sets randomly. What is the probability that each set contains exactly 13 red cards?

I am having trouble even being sure where to begin on this problem. Can someone help me through the steps. I know how to find the number of total possible sets of 26 cards, i.e. 52 choose 26. But I don't know what to do after that.

We can reframe the question slightly as choosing 26 cards from 52 and asking the probability that there are exactly 13 red cards among the 26 we chose.

So, how many ways are there to choose 13 red cards out of 26, and how many ways are there to choose 13 black cards out of 26?