Question

In the school of business and economics there are 7 professors teaching business and 7 teaching economics. A committee of 3 business professors and 2 economics professors is to be formed for the purpose of curriculum development. In how many ways can this committee be formed if any one of the business professors and any of the economics professors can be included in the committee

Answer 1

To form the committee from 7 business professors and 7 economics professors, 35 ways exist to choose 3 business professors and 21 ways to choose 2 economics professors. Multiply these together to get 735 possible committees.

Step-by-step explanation:

The student's question involves forming a committee of professors for curriculum development, consisting of 3 business professors and 2 economics professors.

With 7 business professors available, the number of ways to choose 3 is given by the combination formula C(n, k) = n! / (k! * (n-k)!), where n is the total number of items to choose from, k is the number of items to choose, and ! denotes factorial.

Similarly, for the 7 economics professors, we find the number of ways to choose 2.

To calculate the total number of ways to form the committee

1. Select 3 business professors from 7: C(7, 3) = 7! / (3! * (7-3)!) = 35 ways.
2. Select 2 economics professors from 7: C(7, 2) = 7! / (2! * (7-2)!) = 21 ways.

Finally, multiply the two results to get the total number of different committees that can be formed: 35 * 21 = 735 possible committees.