Question

How many different committees can be formed of 10 professionals, each containing at least 2 Project Managers, at least 3 Team Leaders and 1 Vice President.

Answer 1

Number of committees that can be formed of 10 professionals , each containing at least 2 Project Managers, at least 3 Team Leaders and 1 Vice President is given by

                           =Number of combination of 10 things out of 2 are of same kind , 3 are of different kind, and 1 is of other kind.

                  =  $\frac{10!}{3! \times2! \times1!}$

                   =$\frac{10\times9\times8\times7\times6\times5\times4\times3\times2}{6\times2}$

                 = 5040×60

                  = 302400