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?

Question

Kelvin Liu

Mathematics

9 July, 06:57

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?

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Answers (1)

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Vincent Wells · 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