Question

A restaurant offers 12 different appetizers. How many ways can a group of friends share 3 different appetizers?

Answer 1

220

Explanation:

This is a Combinations question, in that we don't care what order the appetizers are chosen by which friend, only that 3 different appetizers are present on the table for the friends to share.

The formula for Combinations is:

`C_(n,r)=(n!)/((r!)(n-r)!)`

substituting in values (n is the number of available options, which is 12, and r is the number of options we are choosing, which is 3), we get:

`C_(12,3)=(12!)/((3!)(12-3)!)`

and now solve:

`(12!)/((3!)(12-3)!)=(12xx11xx10xxcancel9!)/((3!)(cancel(9!)))=(cancel12^2xx11xx10)/cancel6=2xx11xx10=220`