tarek99 wrote:

John has to paint a wall with seven horizontal stripes. He only has enough paint for four red stripes, four blue stripes, and four yellow stripes. If he can use at most two colors, how many different ways can he paint the wall?

(A) 420

(B) 210

(C) 84

(D) 35

(E) 7

I'm getting (B) 210.

(i) Given the limitations, the only possible combination is 4 stripes of one colour, and 3 of another, therefore 6 colour schemes (4r3b, 3r4b, 4y3b, 3y4b, 4r3y, 3y4r)

(ii) To calculate the arrangements of stripes on the wall = 7c4 arrangements (you "arrange" the 4 stripes of one colour, and the 3 other stripes go into the other spaces)

(i)*(ii) = 6*35 = 210