Question

Before you is a pile of 8 blocks: 4 are white, 3 are yellow, and 1 is purple. By placing the blocks side by side in a straight line, how many different color patterns could you make?

Answer 1

@Zepdrix

Answer 2

@Hero

Answer 3

if all the 8 blocks were different colors it would be simple, just 8 factorial
but since you have 4 white blocks and 3 yellow blocks, there will be fewer than 8! permutations because you can switch white blocks with white blocks, and still get the same pattern, same thing with yellow blocks

so to account for this, you just have to divide

8!/(4! 3!)

Answer 4

280


40,320


144


6,720

Answer 5

right, evaluate what 8!/(4! 3!) and you will end up with one of the choices.