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' ??
Accepted Solution
A:
The function "choose k from n", nCk, is defined as Β 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. Β 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. Β (2C1)*(5C2)*(5C2) = 2*10*10 = 200 You can put 200 different teams on the floor.