Chapter 8.5, Problem 69E

To determine

To find: the number of ways of selection six member committees are possible.

Answer to Problem 69E

Numbers of ways to selection of 6 committee members is 462000.

Explanation of Solution

Given Information:

A six member research committee to be formed having one administrator, three faculty members, and two students. There are seven administrators, 12 faculty members, and 25 students in contention for the committee.

Calculation:

One of seven administrator mean,

  ${}_7{C}_1=\frac{7!}{\left(7-1\right)!1!}=7$

Three of twelve faculty members mean,

  ${}_{12}{C}_3=\frac{12!}{\left(12-3\right)!3!}=220$

Two of twenty students mean,

  ${}_{25}{C}_2=\frac{25!}{\left(25-2\right)!2!}=300$

Number of ways to select 6 committee members is

  ${}_7{C}_1{\times }_{12}{C}_3{\times }_{25}{C}_2=7\times 220\times 300=462000$

Hence numbers of ways to selection of 6 committee members is 462000.