# I have 4 colors of cubes: red, yellow, blue and green. How many variants have I got to build a tower of 6 blocks?

I have 4 colors of cubes: red, yellow, blue and green. How many variants have I got to build a tower of 6 blocks?

My approach: We have $4$ variants for each block in the tower, so that we get $4^6$ and we need to divide by the amount of permutations that is $6!$, so that we get $4^6/6!$

Am I right?

• I would say a tower has a distinguishable top and bottom, so I think every different ordering represents a different tower, and so I wouldn't divide by anything. Also please check your title: you have 4 colors .. – Bram28 Apr 4 '18 at 17:01
• Do you also have an infinite number of cubes of a given color? – user170231 Apr 4 '18 at 17:11
• $4^6/6!$ is not an integer. – Barry Cipra Apr 4 '18 at 17:41

The $6!$ part is incorrect. That would be the number of ways to order six distinguishable blocks, which doesn't apply here.
The answer before you took this detour is correct: $4^6$.