## Related questions with answers

A drawer contains 6 red socks, 4 green socks, and 2 black socks. Two socks are chosen at random. What is the probability that they match?

Solution

VerifiedDEFINITIONS

Fundamental 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 multinomial coefficients: The number of ways in which ways $n$ objects can be grouped into $r$ classes with $n_i$ the size of the $i$th class are

$\left(\begin{matrix}n \\ n_1\: n_2 \: .... \: n_r\end{matrix}\right)=\dfrac{n!}{n_1!n_2!...n_r!}$

Definition permutation (order is important):

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

Definition combination (order is not important):

$C_{n,r}=\left(\begin{matrix}n\\ r\end{matrix}\right)=\dfrac{n!}{r!(n-r)!}$

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

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