Richard has to paint a mural with seven horizontal stripes. He only ha

Question

Richard has to paint a mural with seven horizontal stripes. He only has enough paint for four red stripes, four blue stripes, four white stripes, four black stripes, and four yellow stripes. If his patron wants at most two different colors in the mural, how many different ways can he paint the wall?

(A) 120
(B) 350
(C) 700
(D) 2,520
(E) 5,040

Are You Up For the Challenge: 700 Level Questions

(A) 120
(B) 350
(C) 700
(D) 2,520
(E) 5,040

Are You Up For the Challenge: 700 Level Questions

ScottTargetTestPrep · Accepted Answer

Since Richard needs to paint 7 stripes, he must use at least two colors since each color of paint is enough for only 4 stripes. However, since his patron wants at most two colors, he must use exactly two colors. The number of ways he can use 2 colors from 5 available colors is 5C2 = 10. For the pair of colors he chooses, he can paint 4 stripes of one color and 3 stripes of the other or vice versa. For example, if he chooses red and blue, he can paint 4 red stripes and 3 blue stripes or 3 red stripes and 4 blue stripes. Therefore, for a pair of colors, he has 2 choices to paint by the number of stripes of each color from the pair. Finally, once he has picked 2 colors and the number of stripes he’s going to paint with each color, there are 7!/(4! x 3!) = (7 x 6 x 5 x 4!)/(4! x 3 x 2) = 7 x 5 = 35 ways to paint the wall with the same 2 colors and the same number of stripes by each color. Therefore, in total, there are 10 x 2 x 35 = 700 different ways to paint the wall.

Answer: C

Archit3110 · Answer

total color options 5 out of which 2 are to be chosen so we have 5c2 ; 10 ways
and for 7 color stripes; they can be chosen in 7!/4!*3! * 2c1 = 70 ways
total possible colors = 70*10 ; 700
IMO C

nick1816 · Answer

The only possible combination for 7 horizontal stripes= 4 stripes of 1 color+ 3 strips of another color

So we need 2 colors; number of ways to select 2 color=5C2=10

Total possible arrangements=  10*\frac{7!}{4!*3!}*2! =700

mohit2492 · Answer

The answer will be 700 as 7C4 for selecting stipes 5C1 for the first color and 4C1 for the second color.
 so together 7C4 X 5C1X 4C1=700

brains · Answer

At most 2 colours means that we can use either one or only two colours. Since one colour is not enough as each colour is only sufficient to paint 4 stripes, we have to use 2 colors. The only possibility is 4 stripes of one colour and 3 stripes of another colour. Now ,we have 5 colours to chose for the first 4 stripes, hence 5 ways. Once chosen, we have 4 colours to chose for 3 stripes, hence 4 ways. So we can choose colours in 5 x 4 = 20 ways such that each colour represents 4 and 3 stripes.one of the arrangement will look like this BBBBGGG. Now just think about it , these 7 stripes can itself be arranged. It can be BGGBGBB or other combinations. So these 7 stripes can be arranged in 7C4 ways which will be 35 ways. Thus total arrangements will be 35 x 20 = 700 ways. Hence C is the answer

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