Statistics HELLLP

Question

How many ways can 3 republicans 2 democrats and 1 independent  be chosen from 10 republicans 8 democrats and 5 independents to fill all 6 positions on the city council

Answer 1

Let (n C r) = n! / [r! (n-r)!]

 

(10 C 3) x (8 C 2) x (5 C 1)

= (10! / 3!7!) x (8! / 2!6!) x (5! / 1!4!)

= 120 x 28 x 5

= 16,800 different combinations