In how many ways can a committee of four men and five women

In how many ways can a committee of four men and five women be formed from a group of seven men and seven women? How many different committees can be formed from 5 professors and 15 students if each committee is made up of 2 professors and 10 students? The U.S. Senate of the 109th Congress consisted of 55 Republicans, 44 Democrats, and 1 independent. How many committees can be formed if each committee must have 4 Republicans and 3 Democrats?

Solution

39 ) Repub ----55

Demo ----- 44

Independent ---- 1

Selecting 4 republicans ----55C4

Democrats ------ 44C3

Nos. of committees that can be formed = 55C4*44C3 = 55!/(4!*51!) * 44!/(3!*41!) =

341055*13244 = 4516932420