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A drawer of socks contains seven black socks, eight blue socks, and nine green socks. Two socks are chosen in the dark. a. What is the probability that they match? b. What is the probability that a black pair is chosen?

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Fundamental counting principle: If one event can occur in mm ways and a second event can occur in nn ways, the number of ways the two events can occur in sequence is then mnm\cdot n.

Definition permutation (order is important):

Pn,r=n!(nr)!P_{n,r}=\dfrac{n!}{(n-r)!}

Definition combination (order is not important):

Cn,r=n!r!(nr)!C_{n,r}=\dfrac{n!}{r!(n-r)!}

with n!=n(n1)...21n!=n\cdot (n-1)\cdot ...\cdot 2\cdot 1.

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