Hänschen has a dream where he finds himself in a shop with an infinite supply of marbles. He is allowed to choose n marbles from the shop, which has marbles of k different colors. There are infinitely many marbles of each color. Hänschen wants to ensure that he selects at least one marble of each color, but there are numerous possibilities for his selection. However, before he can make a decision, he wakes up. Now, he seeks your help in determining the number of possible selections he could have made. It is important to note that marbles of the same color cannot be distinguished from each other, and the order of the marbles is not significant.