Question

A school needs to hire 3 Math teachers, 4 science teachers, and 2 english teachers. They have 5 applications for math 7 applications for science and 9 applications for English. How many different ways can the principal meet his staffing needs for the upcoming school year?

A.)(5C3) (7C4) (9C2)
B.)(5P3) (7P4) (9P2)
C.)21C9
D.)21P9

Answer 1

Answer: Choice A

(5C3)*(7C4)*(9C2)

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Step-by-step explanation:

We have 5 applications for math teachers, but only 3 slots to fill. Order does not matter, so there are 5C3 different combinations possible. The C refers to the combination formula as shown below

`_nC_r = (n!)/(r!(n-r)!)`

Similarly, we have 7 science teacher applications, and 4 slots to fill. There are 7C4 different combinations here.

Lastly, there are 9 English teacher applications and 2 slots to fill giving 9C2 ways to do this.

We then multiply out those three expressions getting the final answer shown in choice A.