Question

How many color arrangements are possible by placing 3 red balls, 5 green balls, and 2 yellow balls in a row?
color arrangements

Answer 1

We have total (3+5+2) = 10 balls, of which 3 are red, 5 are green & 2 are yellow.

So, these 3 red balls can permute in a row in 3! ways & corresponding to each of those permutations, the 5 green balls can permute in 5! ways in a row and corresponding to each of those combined permutations, the 2 yellow balls can permute in 2! ways in a row.

So, the total number of identical permutations are 3!5!2!

So, the total number of possible color arrangements of the balls in a row, are,

10!/(3!5!2!) = 10.9.8.7.6/(6.2) = 2520