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# John has to paint a wall with seven horizontal stripes. He only has en

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Re: John has to paint a wall with seven horizontal stripes. He only has en [#permalink]
Bunuel 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

Are You Up For the Challenge: 700 Level Questions

Since only two colors has to be used out of three, number of ways to select a combination of two colors out of three = Number of ways to select a color out of three * number of ways to select a color out of remaining two color.
= 3 * 2 = 6

Now, ways to arrange 7 stripes = 7!
Ways in which the two color(whatever they may be) stripes are arranged = 4!*3!
Ways to arrange 7 stripes with 2 colors = $$\frac{7!}{4!*3!}$$

Total number of ways to arrange 7 stripes with 2 colors = $$\frac{7!}{4!*3!}*6 = 210$$
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Re: John has to paint a wall with seven horizontal stripes. He only has en [#permalink]
I have an issue. Where in the question it is written that he has to use 4+3 combination to paint the stripes. He may use 6+1, 5+2, 4+3, 3+4, 5+2, 6+1 Combinations also. And accordingly combinations will increase. Please suggest if I am wrong somewhere.
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Re: John has to paint a wall with seven horizontal stripes. He only has en [#permalink]
memayank wrote:
I have an issue. Where in the question it is written that he has to use 4+3 combination to paint the stripes. He may use 6+1, 5+2, 4+3, 3+4, 5+2, 6+1 Combinations also. And accordingly combinations will increase. Please suggest if I am wrong somewhere.

memayank
Read the question carefully and you would know where you are going here.
Quote:
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

The max. stripes a color can have is 4. So, how come '6 + 1' or '5 + 2' OR vice-a-versa is possible.
Rest i guess you know how to solve.

Thanks..!!
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Re: John has to paint a wall with seven horizontal stripes. He only has en [#permalink]
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Re: John has to paint a wall with seven horizontal stripes. He only has en [#permalink]
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