A company has 6 officers and 4 directors (10 different people). In how many ways can a committee of 4 be selected from these 10 people so that the following hold? (a) 2 members are officers and 2 are directors. ways (b) 3 members are officers and 1 is a director. ways (c) All the members are officers. ways (d) There are no restrictions. ways.

There are 12 teams in a league. In how many ways can the teams finish first, second, third, and fourth? (Assume there are no ties.) ways

There are 4 vacancies on the scholarship committee at a certain university. In order to balance the men and women on the committee, 1 woman and 3 men are to be appointed. In how many ways can this be done if the following are available to serve? (a) 9 men and 8 women ways(b) 4 men and 5 women ways

An employee group requires 6 people be chosen for a committee from a group of 16 employees. The employee group has 6 women and 10 men. How many ways are there where 3 of the people chosen for the committee are women and 3 people chosen for the committee are men? 2400 The committee requires that exactly 2 people from Human Resources serve on the committee. There are 5 people in Human Resources. How many ways are there where exactly 2 of the people chosen for the committee are from Human Resources?

A class has 32 students. In how many different ways can four students form a group for an activity? (Assume the order of the students is not important.) C.. There are different ways that the four students can form a group for an activity. (Type a whole number.)

In how many ways can a committee of three men and four women be formed from a group of eleven men and ten ​women?