Question

Suppose we want to choose 6 colors, without replacement, from 12 distinct colors.A) How many ways can this be done, if the order of the choices IS relevant?B) How many ways can this be done, if order pf the choices is NOT relevant

Answer 1

Okay, here we have this:

A)

Considering the provided information we are going to replace in the following equation:

$nCr=\frac{n!}{(n-r)!r!}$

Replacing we obtain:

$\begin{gathered} _{12}C_6=\frac{12!}{(12-6)!6!} \\ _{12}C_6=\frac{12!}{6!\cdot\:6!} \\ _{12}C_6=\frac{12\cdot\:11\cdot\:10\cdot\:9\cdot\:8\cdot\:7}{6!} \\ =\frac{665280}{6!} \\ =\frac{665280}{720} \\ =924 \end{gathered}$

Finally we obtain that the number of ways considering that the order of the choices IS relevant is 924.