SEC17 6 Suppose you are managing 14 employees and you need t

SEC17) #6

Suppose you are managing 14 employees, and you need to form three teams to work on different projects. Assume that all employees will work on a team, and that each employee has the same qualifications/skills so that everyone has the same probability of getting chosen. In how many different ways can the teams be chosen so that the number of employees on each project are as follows: 8, 3, 3

Solution

for the first team, : 14C8 ways to pick a team

for the second team: 6C3 ways to pick a team (as 8 are no longer available)

for the third team: 3C3 = 1 way to pick a team

number of ways to make 3 teams =number of ways to make Team 1 * Ways for Team 2 * Ways for Team 3 = 14C8 * 6C3 * 3C3