A restaurant has 6 different desserts. Find the number of ways a customer can choose: a) 1 dessert; b) 2 of the desserts; c) 3 of the desserts.
a) Since there is only one choice to be made, the customer can choose any one of the 6 different desserts. Therefore, there are 6 ways to choose 1 dessert.
b) To choose 2 of the desserts, the customer must first choose one dessert out of the 6, and then choose another dessert out of the remaining 5. But since the order in which the desserts are chosen doesn't matter (choosing Dessert A and then Dessert B is the same as choosing Dessert B and then Dessert A), we need to divide by 2 to avoid counting each pair twice. So the number of ways to choose 2 desserts is:
6 x 5 / 2 = 15
c) To choose 3 of the desserts, the customer must first choose one dessert out of the 6, then choose a second dessert out of the remaining 5, and finally choose a third dessert out of the remaining 4. However, again we must divide by the ways the desserts can be ordered:
6 x 5 x 4 / (2 x 3) = 60
Therefore, there are 6 ways to choose 1 dessert, 15 ways to choose 2 desserts, and 60 ways to choose 3 desserts.