Question

A friend of mine is giving a dinner party. His current wine supply includes 11 bottles of zinfandel, 10 of merlot, and 9 of cabernet (he only drinks red wine), all from different wineries.

(a) If he wants to serve 3 bottles of zinfandel and serving order is important, how many ways are there to do this?

Answer 1

There are 990 different ways to serve 3 bottles of zinfandel when order is important, calculated using the formula for permutations without repetition P(11, 3) = 11! / (11 - 3)!, which equals 11 x 10 x 9.

Step-by-step explanation:

The student's question concerns combinatorics, a branch of mathematics dealing with counting combinations and permutations. Specifically, the question asks for the number of ways to serve 3 bottles of zinfandel when serving order is important, which is a problem of permutations.

To solve this, we apply the formula for permutations without repetition, given by P(n, r) = n! / (n - r)! where n is the total number of items to choose from, and r is the number of items to choose.

Here, the friend has 11 bottles of zinfandel and wants to serve 3 bottles:

P(11, 3) = 11! / (11 - 3)! = 11! / 8! = 11 × 10 × 9 = 990

Therefore, there are 990 different ways to serve 3 bottles of zinfandel in a particular order.