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?

Correct answer marked below

420

210

Correct

You can see the correct answer above. Sign in for free to unlock the complete worked solution.

Get detailed analytics, unlock full explanations, and move up difficulty tiers as you practice.

Explanation

Preview

Official Explanation

Official

Number of ways to select 2 colors out of 3 =

^3C_2 = 3

Number of ways to select 1 color for 4 stripes and the other for 3 stripes = 2

Total possible arrangements of 7 stripes =

\frac{7!}{4! \times 3!} = 35

…

Comments

Be the first to share your thoughts and help others understand it better.

What this question tests

Whether you can count arrangements and selections correctly — permutations vs. combinations.

Overcounting: treating a selection as ordered when order does not matter, or forgetting to divide by duplicates.