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 choosen. 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

60060 different ways that teams can be chosen

Step-by-step explanation:

Given data

employees n = 14

team = 3

each project employees

n (1) = 8

n (2) = 3

n (3) = 3

to find out

how many different ways can the teams be chosen

solution

we know according to question all employees work on a team so

select ways are = n! / n (1) ! * n (2) ! * n (3) ... 1

here n! = 14! = 14 * 13 * 12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1

and n (1) ! = 8! = 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1

n (2) ! = 3! = 3 * 2 * 1

n (3) ! = 3! = 3 * 2 * 1

so now put all these in equation 1 and we get

select ways are = (14 * 13 * 12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1) / (8 * 7 * 6 * 5 * 4 * 3 * 2 * 1) * (3 * 2 * 1) * (3 * 2 * 1)

select ways are = (14 * 13 * 12 * 11 * 10 * 9) / (3 * 2 * 1) * (3 * 2 * 1)

select ways are = 2162160 / 36

select ways are = 60060

60060 different ways that teams can be chosen