Answer:
We conclude that he coach can choose 252 lineups.
Step-by-step explanation:
We have three pure centers, four pure forwards, four pure guards and one swing- man who can play either guard or forward.
First case: swing- man play guard.
So now we count the number of combinations: to select from 3 centers 1 center, from 4 forwards to choose 2, and from 4 from the guards to choose 1.
Second case: swing- man play forward.
So now we count the number of combinations: to select from 3 centers 1 center, from 4 forwards to choose 1, and from 4 from the guards to choose 2.
Third case: swing- man not play.
So now we count the number of combinations: to select from 3 centers 1 center, from 4 forwards to choose 2, and from 4 from the guards to choose 2.
Now, we get 72+72+108=252.
We conclude that he coach can choose 252 lineups.