Question

The chair of the Department of Mathematics and Statistics needs to appoint a faculty committee consisting of 5 mathematics and 4 statistics faculty. There are 23 mathematics and 14 statistics faculty members in the department. In how many ways can he select a committee? Setup the numerical expression using fractions, factorials, etc. but you do not need to evaluate it.

Answer 1

There are 27,720 ways to select the committee

Explanation:

First, it is necessary to know how many ways are there to select 3 members, if there are 9 members of the mathematics department. This can be found using the following equation:

Where nCk gives as the number of ways in which we can select k elements from a group of n elements. So, replacing n by 9 and k by 3 members, we get:

So, there are 84 ways to select 3 members from 9 members of the mathematics department.

At the same way, we can calculate that there are 330 ways to select 4 members from the 11 that belong to the Computer science department as:

Finally the total number of ways in which we can form a committee with 3 faculty members from mathematics and 4 from the computer science department is calculated as:

9C3 * 11C4 = 84 * 330 = 27,720