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

Answer:60060 different ways that teams can be chosenStep-by-step explanation:Given data employees n  = 14team = 3 each project employees n(1) =  8n(2) = 3n(3) = 3to find out how many different ways can the teams be chosensolutionwe know according to question all employees work on a team soselect ways are = n! / n(1) ! × n(2) ! × n(3)     ....................1here  n! = 14! = 14 × 13 ×12 ×11 ×10 ×9 ×8 ×7 ×6 ×5 ×4 × 3× 2× 1and n(1)! = 8! =  8 ×7 ×6 ×5 ×4 × 3× 2× 1n(2)! = 3! =  3× 2× 1n(3)! = 3! =  3× 2× 1so 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 / 36select ways are = 6006060060 different ways that teams can be chosen