Comparison to flipping a coin 26 times
I agree with emp1346's answer. I thought it might be interesting to compare this question to a similar coin toss probability question.
The probability of getting n red cards when drawing 2 n cards from a size 4 n deck is
C(2*n, n)^2/C(4*n, 2*n) ~= Sqrt(2/Pi/n).
The probability of getting n heads when flipping a coin 2 n times is
C(2*n, n)/2^n ~= Sqrt(1/Pi/n).
So the probability of getting n heads is about the probability of getting n red cards divided by Sqrt(2). Hmmm.
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