Question #1886

There are ten different pairs of socks, you take out 6 socks, what is the probability that you will be left with 7 whole pairs, the probability that you'll be left with 4 pairs?

Expert's answer

The probability that you will be left with 7 whole pairs is equal to the probability that you take 3 whole pairs :

P = C^{3}_{10} / C^{6}_{20}

The probability that 4 pairs will be left is

P = 2^{6} C^{6}_{10} / C^{6}_{20}.

P = C

The probability that 4 pairs will be left is

P = 2

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