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

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Richard has to paint a mural with seven horizontal stripes. He only ha [#permalink]

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New post 07 Sep 2016, 12:25
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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
[Reveal] Spoiler: OA

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Re: Richard has to paint a mural with seven horizontal stripes. He only ha [#permalink]

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New post 07 Sep 2016, 13:21
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Tricky one.

Number of ways to choose 2 colors among 5 - 5c2
Number of ways that the chosen colors can be painted for 7 horizontal stripes - 2 (either (4,3) or (3,4))

Now the order,
the number of ways in which a particular color among the 2 chosen colors can be painted for 4 stripes is - 7c4
[Note: We don't need to calculate the ways for the remaining 3 stripes as they are obvious and already counted under this]

Total number of combinations - 5c2 * 2* 7c4 = 700

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Richard has to paint a mural with seven horizontal stripes. He only ha [#permalink]

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New post 12 Nov 2017, 20:14
duahsolo wrote:
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

This is first a combination and then permutation problem


1. There are 5 colors. Number of ways of choosing 2 colors out of 5 is 5C2=10
2. One color can at the most be used for 4 stripes . So just one color cannot be used and 2 colors have to be used. If 2 colors have to be used, 4 strips can be of 1 color and 3 stripes another color.
3. Number of permutations of 2 color combination for 4 stripes and 3 stripes is 2*(7!/(4!*3!)=70. We are multiplying by2 because either one of the 2 colors can be used to paint 4 stripes.
4. Total number of ways of painting = 10*70=700

We can relate the problem to the familiar setting of word and letters. 7 stripes correspond to 7 letters in a word. There are 5 colors and so 5 letters and 4 each.

So the problem is how many 7 letter word can be formed with utmost 2 letters and only a maximum of 4 repetitions of 1 letter can be used?
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Re: Richard has to paint a mural with seven horizontal stripes. He only ha [#permalink]

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New post 17 Nov 2017, 18:43
ways of choosing 2 colors among 5 5C2 = 10
ways to paint the wall by using one of those selected colors 7C4=35
2 colors 35*2=70
total ways 35*2*10=700

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Re: Richard has to paint a mural with seven horizontal stripes. He only ha   [#permalink] 17 Nov 2017, 18:43
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