Question

Please explain your answer. Thank you!!

Answer 1

Answer:

(A) 180

Step-by-step explanation:

We have to treat those player selections as independent events, since one doesn't influence the other (the fact you chose Joe as a guard, shouldn't have an influence on who'll pick as center, unless there's bad blood between some players... but that's a whole other story).

So, how many ways to pick 2 guards from a selection of 4?  The order doesn't seem to matter here, since they don't specify for example that Joe can only play on the left side).  So, it's a pure combination calculation:

$C(4,2) = \frac{4!}{2! * (4 - 2)!} = \frac{24}{2 * 2} = 6$

C(4,2) = 6.

How many ways to pick the 2 forwards from a group of 5?  Using the same calculation, we get:

C(5,2) = 10.

And of course, the coach has 3 ways to pick a center player from 3.

Then we multiply the possible ways to pick guards, forwards and center...

6 * 10 * 3 = 180 ways.