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Maslowich
3 years ago
5

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 Offic

e 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
Mathematics
1 answer:
NikAS [45]3 years ago
3 0

Answer:

55,440 ways

Step-by-step 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=\frac{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=\frac{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

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