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?

_________________

Srinivasan Vaidyaraman

Sravna

http://www.sravnatestprep.com/regularcourse.php

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