37. In how many ways can a committee of four men and five women be formed from a group of seven men and seven women?
38. 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?

A committee of three is chosen from a group of 20 people. How many different committees are possible, if (a) the committee consists of a president, vice president, and treasurer? (b) there is no distinction among the three members of the committee?

During the 109th Congress (2005-2006), the U.S. Senate had a total of 99 Democrats and Republicans. There were 11 more Republicans than Democrats. How many Democrats and Republicans were there in the Senate?

A committee of 6 people is to be chosen from a group consisting of 7 men and 8 women. If the committee must consist of at least 3 women and at least 2 men, how many different committees are possible?

Graph a sample space for the experiments: Choosing a committee of 2 from a group of 5 people

A city council consists of six Democrats and four Republicans. If a committee of three people is selected, find the probability of selecting one Democrat and two Republicans.

Answer for the sequence $a$ defined by $a_n=n^2-3n+3$, $n\geq 1$. Find $\sum_{i=1}^4 a_i$.

There are 7 women and 5 men in a department. How many ways can a committee of 4 people be selected? How many ways can this committee be chosen if there must be 2 men and 2 women on the committee? How many ways can this committee be selected if there must be at least 2 women on the committee?

In how many different ways can we select a committee consisting of 3 engineers, 2 physicists, and 2 computer scientists from 10 engineers, 5 physicists, and 6 computer scientists? First guess.

There are four Democrats and five Republicans on the county commission. From among their group, they will choose a committee of two Democrats and two Republicans to examine a proposal to purchase land for a new county park. How many four-person groups are possible?

A group of 15 people wants to form a committee consisting of a chair, vice chair, and three additional members. How many different committees can be formed?

A committee of 5 is chosen from 10 men and 6 women. Determine the number of ways of selecting the committee if: a. there are no restrictions b. it must contain 3 men and 2 women c. it must contain all men d. it must contain at least 3 men e. it must contain at least one of each sex.

A group consists of 5 men and 8 women. A committee of 4 is to be formed from this group, and policy dictates that at least 1 woman be on this committee. How many committees can be formed that contain at least 1 man?

In how many ways can we select a committee of three from a group of 11 persons?