Question

Out of 50 basketball players trying to make a team, 5 will be chosen. 36 of the 50 are seniors and the remaining players are juniors. The coach wants 2 seniors and 3 juniors to make the team. In addition, the coach wants a senior who makes the team to be a captain. In how many ways can the coach select such a team from the 50 players who try out?

Answer 1

Answer:   5503680

Step-by-step explanation:

The coach wants  2 senior out of 36 so he have

C₃₆,₂   =  36!/( 36 - 2 )!     = 36*35*34!/34!    =  36 * 35   = 1260

possibilities

Now he also wants 3 juniors out of 14

C₁₄,₃  =   14!/ (14- 3)!      =  14*13*12*11!/11!     =  14*13*12  = 2184

Now for each pair of senior (from 1260 outcomes) coach has 2184 possiblities therefore

Coach has

2184 * 1260 = 2751840    possibilities to choose from

Again as there are 2 senior to choose for captain we have to multiply by 2 to get the total  ways the team could be

2751840*2  = 5503680