Question

A basketball team contains 16 players. If 5 people can be on the court at one time, how many different groups can be selected to be on the court?

Answer 1

Explanation:

there are no repetitions (there are not multiple copies of the same player).

and the sequence (or order) of the selected players does not matter (p1, p2, p3, p4, p5 is the same as e.g. p3, p5, p1, p2, p4).

so, we have the combinations of 5 out of 16 items :

C(16, 5) = 16!/(5! × (16-5)!) = 16!/(5! × 11!) =

= 16×15×14×13×12/(5×4×3×2) =

= 4×3×14×13×2 = 4,368

there can be 4,368 different groups.