I was explaining Combinatorial Analysis to a friend who had never had it, and when I got to Permutations of Indistinguishable Objects and told him the formula for it, he asked "Why do you divide?"
I thought about it for a second, and realized that when I was taught this, I was really essentially told "You have to get rid of the extras, and you do that by dividing" and I accepted it. I told him that, and he accepted it, but it's bugging me now. How was this conclusion reached? Is there some kind of proof somewhere that shows why this is true?