A student council consists of 12 students containing 7 men a…
A student council consists of 12 students containing 7 men and 5 women. (1) In how many ways can a committee of 5 be selected from the membership of the council? (2) How many committees of 5 contain 2 men and 3 women? (3) Two council members have the same major and are not permitted to serve together on a committee. How many ways can a committee of 5 be selected from the membership of the council? (4) How many 5-person committees contain at least one woman? (Please fill each blank with an integer.)