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Suppose that you have 20 different letters and 10 distinctly addressed envelopes. The 20letters consist of...

Suppose that you have 20 different letters and 10 distinctly addressed envelopes. The 20letters consist of 10 pairs, where each pair belongs inside one of the 10 envelopes. Suppose that you place the 20letters inside the 10 envelopes, two per envelope, but at random. What is the probability that exactly 3 of the 10 envelopes will contain both of the letters which they should contain?

I know the answer is [ (20-2*3)! / 2^(10-3) ] / [20! / 2^10] but i am not sure why it becomes this formula. Could you explain why?

Thank you

Math   Statistics-And-Probability   
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