Question

your car stereo can be programmed to hold six radio stations of your choice. There are 9 stations you really like. How may different ways can you program your six buttons with different collections of your favorite stations?

Answer 1

Combinations


nCr
you have n items and how many ways are there to chose r of them

nCr=$\frac{n!}{r!(n-r)!}$
remember than n! means n times all numbers before like
3!=3*2*1, 5!=5*4*3*2*1
9 stations, how many ways are there to chose 6 of them
9C6=$\frac{9!}{6!(9-6)!}$=
$\frac{9!}{6!(3)!}$=
$\frac{9*8*7}{3!}$=
$\frac{9*8*7}{3*2*1}$=
$\frac{3*4*7}{1}$=
84

84 ways