sana.noor 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
OA is B
Each color may constitute at most 4 stripes.
Thus, of the 7 stripes:
4 stripes must be of ONE of the 2 colors selected.
The remaining 3 stripes must be of THE OTHER color selected.
Number of ways to select 4 stripes from 7 options = 7C4 = (7*6*5*4)/(4*3*2*1) = 35.
Number of color options for these 4 stripes = 3. (Any of the 3 colors.)
Number of color options for the remaining 3 stripes = 2. (Either of the 2 remaining colors.)
To combine these options, we multiply:
35*3*2 = 210.
The correct answer is
B.
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