Suppose we want to choose 6 colors, without replacement, from 9 distinct colors.

Question

Suppose we want to choose 6

 colors, without replacement, from 9

 distinct colors.

(a)	How many ways can this be done, if the order of the choices is not taken into consideration?
(b)	How many ways can this be done, if the order of the choices is taken into consideration?

Answer 1

Answer for a is

N_permutations = _nP_r = n!/ (n-r)!

N_permutations = ₉P₆ = 9!/(9-6)! = 9*8*7*6*5*4 = 60480

Answer for b is

N_combinations = _nC_r = n!/((n-r)!r!)

N_combinations = ₉C₆ = 9!/((9-6)!6!) = (9*8*7)/(3*2*1) = 84