I have 3 yellow pieces of paper, 4 blue, 5 brown, and 2 green. I know that I have to do some sort of permutation calculation since a yellow piece in index 1 would be considered the same as a different yellow piece in the same index.
My current solution is : $\dfrac{14!}{3! 4! 5! 2!}=2522520.$ However, I don't know if I've done this correctly.
I was absent for the lesson on how to resolve this and cannot seem to wrap my head around it. Any explanation would be appreciated.
First assume all 14 papers are considered all different (i.e. papers in same color are indexed with different numbers). Then there are total $$14!$$ cases. Now assume those three yellow papers are considered same. You know there are $3!$ ways to arrange three 'indexed' yellow papers. Now that those $3!$ cases should be merged to 1 case, the total number of cases is now $$\frac{14!}{3!}$$. You do this for four blue papers and now you get $$\frac{14!}{3!4!}$$. You keep doing this to other colors and you get $$\frac{14!}{3!4!5!2!}$$