1 . Consider lineups without x. You have to select
- 2 guards from 5 quards;
- 2 forwards from 3 forwards;
- 1 center from 4 centers.
It can be made in
different ways.
2. Consider lineups with x as guard. You have to select
- 2 guards from 6 quards (one of them must be x);
- 2 forwards from 3 forwards;
- 1 center from 4 centers.
It can be made in
different ways.
3. Consider lineups with x as forward. You have to select
- 2 guards from 5 quards;
- 2 forwards from 4 forwards (one of them must be x);
- 1 center from 4 centers.
It can be made in
different ways.
Therefore, the total number of different lineups is
120+60+120=300.