If the grocery store has 15 different kinds of fruit and 10 different kinds of canned soup, in how many ways can Michael choose 2 different kinds of fruit and 3 different kinds of soup to buy?
To choose 2 different kinds of fruit out of 15, I can use the combination formula: 15 choose 2, which is 15!/(2!13!) = 105. Similarly, to choose 3 different kinds of soup out of 10, I can use the combination formula again: 10 choose 3, which is 10!/(3!7!) = 120. Now, since the choice of fruit and the choice of soup are independent events, I can multiply the number of ways to do each one to get the total number of ways to do both: 105 * 120 = 12600. 