Question

There are ten candidates for a job. The search committee will choose three of them, and rank the chosen three from strongest to weakest. How many different outcomes are possible

Answer 1

720

Explanation:

Since we are choosing a subset of 3 people from a set of 10 people, and arranging the 3 people according to relative strength, the answer can be obtained by computing P(10,3).

P(10,3)=10! / (10-3)!

= 10!/7!

Rewrite 10 ! as

10 * 9 * 8 * 7 ! / 7!

Cancel the common factor of 7 ! and divide ( 10 * 9 * 8 ) by 1

10 * 9 * 8 = 720