How many ways can you align 3 red balls, 2 blue balls and 2 yellow balls in a row given that at the beginning and the end of the row there is a red ball? (balls of the same color aren't unique).
My solution was - since we have to put two red balls at the beginning and end then we need to order only 1 red ball, 2 blue and 2 yellow. Let's say the order matters, then there are 5! = 120 ways to order the balls. Since we counted as though 2 blue balls differ we need to correct that and divide by 2. Same goes for the yellow balls.
Then the answer is 30.
My professor came up with a different way when he published the answer. Simply:
(5 choose 2,2,1) = 30. He didn't explain what this is and how to compute it.
I'm assuming it's an abbreviation for saying - from 5 balls choose 2 blue, 2 yellow and 1 red but can't find any reference to it.
