Question

There are 12 people on the basketball team. How many different 5-person starting lineups can be chosen?
120
792
95,040
3,991,680

Answer 1

If there are 5 specific positions and the order matters then we would have:

12P5 ways, i.e. 12!/(12 - 5)! = 12!/7! = 12 x 11 x 10 x 9 x 8 = 95,040

However, if we just require groups of 5 players where order does not matter we would have:

12C5 ways, i.e. 12!/5!(12 - 5)! = 12!/5!7! = (12 x 11 x 10 x 9 x 8)/(5 x 4 x 3 x 2)

=>11 x 9 x 8 = 792