## Related questions with answers

Question

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?

Solution

VerifiedAnswered 2 years ago

Answered 2 years ago

Step 1

1 of 4Fundamental counting principle: If one event can occur in $m$ ways and a second event can occur in $n$ ways, the number of ways the two events can occur in sequence is then $m\cdot n$.

Definition permutation (order is important):

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

Definition combination (order is not important):

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

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

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