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=
`(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=
`(9!)/(6!(9-6)!)`=

`(9!)/(6!(3)!)`=

`(9*8*7)/(3!)`=

`(9*8*7)/(3*2*1)`=

`(3*4*7)/(1)`=
84

84 ways