Question

11. In how many ways can the 11 identical horses on a carousel
be painted so that three are brown, three are white, and five are
black?

Answer 1

doing the brown, then white, then black
3 Brown starting with 11 possibilities
11*10*9 / (1*2*3) = 165

3 White with 8 remaining possibilities
8*7*6 / (1*2*3) = 56

5 black with the 5 remaining possibilities = 1
5*4*3*2*1 / (1*2*3*4*5)

165 * 56 * 1 = 9240

Doing the black first, we should come up with the same answer
Balck, brown then white

11*10*9*8*7 / (1*2*3*4*5) = 462
6*5*4 / (1*2*3) = 20
3*2*1 / (1*2*3) = 1

462 * 20 *1 = 9240
9240