Answer
$126$
Work Step by Step
Recall the combination formula:
$_{n}C_k=\dfrac{n!}{(n-k)!k!}$
We use combinations instead of permutations in cases where order does not matter. In this case, the order in which team members does not matter, so using combinations is appropriate.
The number of ways of choosing the center player is given by $_{2}C_{1}$ (one player out of two choices). Similarly, the number of ways to choose the guard player is $_{3}C_{2}$ (two players out of three). Finally, the number of forward players we can choose is $_{12-2-3}C_{2}=_{7}C_{2}$ (out of seven players choose two). To get the total number of combinations we multiply the individual combinations above (multiplication principle).
Thus, we have:
$_{2}C_{1}(center)_{3}C_{2}(guards)_{12-2-3}C_{2}(forward)=(2)(3)(21)=126~ways$
