Question:
Hänschen dreams he is in a shop with an infinite amount of marbles. He is allowed to select n marbles. There are marbles of k different colors. From each color, there are also infinitely many marbles. Hänschen wants to have at least one marble of each color, but still there are a lot of possibilities for his selection. In his effort to make a decision he wakes up. Now he asks you how many possibilities for his selection he would have had. Assume that marbles of equal color can’t be distinguished, and the order of the marbles is irrelevant.
Doubt:
After first k marbles,we will be left with n-k spaces,and each space can contain any one of the k different marbles.So each space has k possibilities,like wise (n-k) spaces will have pow(n-k,k). This is my approach.why is it wrong?Please give me a clear explanation.