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.

There are 27,720 ways to select the committee

Step-by-step 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

when rotating a figure 180 degrees, imagine that you are able to take the figure and turn it clockwise or counterclockwise around a center point. to rotate a figure 180 degrees, you will need to apply the rule (x, y) → (-x, -y). start by using a coordinate grid with coordinates for each vertex of the figure. the center point of the coordinate grid is located at (0, 0), which is what you will rotate the figure around. write down the original coordinates of the shape you are going to rotate. then, apply the rule. for example, coordinate (1, 2) becomes (-1, -2). another example would be, coordinate (-4, -2) becoming (4, 2). after you change each original coordinate to the rotated coordinate, you will draw your new figure.

step-by-step explanation:

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