An Example from my Probability Class I Need Help w/

[yellowjack]

A deck of 52 cards is divided into two equal sets randomly. What is the probability that each set contains 13 red cards?

Answer:
You choose 13 of 26 for the first set, and 13 of the remaining 13 for the second set.

26_C_13 * 13_C_13 = # of ways the deck can be split with 13 red cards for each set

52_C_26 = total # of ways that 52 cards can be split into 2 equal sets

26_C_13 * 13_C_13 = 26_C_13, therefore

(26_C_13) / (52_C_26) = answer

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For the first part of this question, are we completely ignoring the black cards here and just finding out how many ways we can pick exactly 13 red cards from the 26 total red cards for one set?

Also for the 52 choose 26, this is total number of ways 26 cards (red and black) grouped together can be chosen for one set of the 52 cards in half. Is there I can do (i.e. double-checking w/ other possible calculations) to assure myself that this value will make sense with the 26_C_13 bit, or should it come as intuitional?

Thanks.