Bred has to paint a wall with 8 horizontal stripes. He has enough paint only for 5 blue, 5 red and 5 white stripes. If he can use at most 2 colors, how many different ways he can paint the wall.

336

Step-by-step explanation:

Required Formulas:-

1. Number of ways to select x things out of n things = ⁿCₓ

2. Number of ways to arrange n things when a things and b things are similar = n! / (a!*b!)

Since we have to choose 8 colors and we are having 3 different colors, it is only possible when we select 2 different colors (e. g. 5 red and 3 blue). To find all possible ways we will have to find all unique arrangements of selected color.

Using formula (1), number of ways to select 2 colors out of given 3 colors = ³C₂ = 3

Using formula (2), finding all unique arrangements when 5 stripes are of one color and 3 stripes are of second color = 8! / (3!*5!) = 56

Suppose, we can choose 5 stripes from red color and 3 stripes from blue color or 5 strips from blue color and 3 strips from red color. So there are 2 possibilities of arranging every 2 colors we choose.

∴ Answer=3*56*2 = 336