Question

Seven candidates are running for three different class offices: president, vice president,
and secretary. In how many ways can the offices be filled with these candidates?

Answer 1

Answer: 210

Work Shown:

7 ways to pick the president.

6 ways to pick the VP

5 ways to pick the secretary

7*6*5 = 210 ways to pick the three people from a pool of seven. Order matters because the positions are different. Note the count down from 7 to 6 to 5 which indicates that any given person cannot run for more than one office.

You can use the permutation formula with n = 7 and r = 3

The permutation formula is $_n P_r = \frac{n!}{(n-r)!}$ where the exclamation marks represent factorials.