Question

A committee consisting of 2 faculty members and 3 students is to be formed. Every committee position has the same duties and voting rights. There are 11 faculty members and 14 students eligible to serve on the committee. In how many ways can the committee be formed?

Answer 1

Answer: 20,020 ways

Step-by-step explanation:

Given : The number of faculty members = 11

The number of students =14

Total number of people are eligible to serve on the committee = $11+14=25$

Now, the number of ways to form a committee consisting of 2 faculty members and 3 students is to be formed will be :-

$^{11}C_{2}\times^{14}C_{3}$

$=\dfrac{11!}{2!9!}\times\dfrac{14!}{3!11!}=20020$

Hence, The committee can be formed in 20,020 ways .