Question

A company is holding a sales contest for its sales reps. 12 sales reps are based in Office A and 7 sales reps are based in Office B. Bonuses of $800, $400, and $200 will be given to the top 3 sales reps in Office AN. Bonuses of $500 and $250 will be given to the top 2 sales reps in Office B. In how many different ways can the bonuses be paid out

Answer 1

55,440 ways

Explanation:

In this situation, since the bonuses are different, the order of the sales reps receiveing the bonus matters, thus permutations should be used.

The number of ways to pay the bonuses in office A (pick 3 out of 12) is:

`A=(12!)/((12-3)!) =12*11*10 = 1,320\ ways`

The number of ways to pay the bonuses in office B (pick 2 out of 7) is:

`B=(7!)/((7-2)!) =7*6 =42\ ways`

Considering both offices, the number of ways to pay out the bonuses is:

`N= A*B = 1320*42\\N=55,440\ ways`