Question

You coach a basketball ball team of 12 players; 5 players must be on the floor at all times; Figuring that every player can play every position.. How many teams can you put on the floor? Now consider that you have 2 centers, 5 guards, and 5 forwards; You must place on the floor at all times 1 center; 2 guards; 2 forwards, How many teams can you 'put on the floor' ??

Answer 1

The function "choose k from n", nCk, is defined as
nCk = n!/(k!*(n-k)!) . . . . . where "!" indicates the factorial

a) No position sensitivity.
The number of possibilities is the number of ways you can choose 5 players from a roster of 12.
12C5 = 12*11*10*9*8/(5*4*3*2*1) = 792
You can put 792 different teams on the floor.

b) 1 of 2 centers, 2 of 5 guards, 2 of 5 forwards.
The number of possibilities is the product of the number of ways, for each position, you can choose the required number of players from those capable of playing the position.
(2C1)*(5C2)*(5C2) = 2*10*10 = 200
You can put 200 different teams on the floor.