Question

A 10-member mathematics department must select one person to chair tha discrete mathematics committee and two other people to co-chair the calculus committee. (a) In how many ways can this be done?

Answer 1

To select a chair for the discrete mathematics committee and two co-chairs for the calculus committee out of a 10-member department, there are 10 ways to select the first chair and 36 ways to select the two co-chairs, for a total of 360 different combinations.

Step-by-step explanation:

To determine the number of ways a 10-member mathematics department can select a discrete mathematics committee chair and two co-chairs for the calculus committee, we need to apply combinatorial methods.

1. First, we select the chair for the discrete mathematics committee. There are 10 members to choose from, so there are 10 different ways to do this.
2. Then, we select 2 co-chairs for the calculus committee. After choosing the chair for the discrete mathematics committee, 9 members remain. The number of ways to choose 2 people out of the remaining 9 is determined by the combination formula C(n, k) = n / (k(n-k)), where n is the total number of members, and k is the number of members to select. So, it would be C(9, 2) which equals 9 / (7), simplifying to 36 ways.

Multiplying the two answers together gives us the total number of ways both selections can be made: 10 x 36 = 360 different ways.

There are 360 different ways to choose a chair for the discrete mathematics committee and two co-chairs for the calculus committee.