There are 10 professors and 20 students out of whom a committee of 2 professors and 3 students is to be formed. Find the number of ways in which this can be done. Further, find in how many of these committees:

Question

Philoid · Accepted Answer

Given that we need to choose 2 professors and 3 students out of 10 professors and 20 students,

Let us assume the choosing the no. of ways be N,

⇒ N = (choosing 2 professors out of 10 professors) × (choosing 3 students out of 20 students)

⇒ N = (¹⁰C₂) × (²⁰C₃)

We know that

And also n! = (n)(n – 1)(n – 2)…………2.1

⇒

⇒ N = 45 × 1140

⇒ N = 51300 ways

It is told that one student is always included.

It is similar to selecting 2 professors and 2 students out of remaining 10 professors and 19 students as 1 student is already selected.

Let us assume the choosing the no. of ways be N₂,

⇒ N₂ = (choosing 2 professors out of 10 professors) × (choosing 2 students out of 19 students)

⇒ N₂ = ¹⁰C₂ × ¹⁹C₂

We know that

And also n! = (n)(n – 1)(n – 2)…………2.1

⇒

⇒ N₂ = 45 × 171

⇒ N₂ = 7695 ways

There are 10 professors and 20 students out of whom a committee of 2 professors and 3 students is to be formed. Find the number of ways in which this can be done. Further, find in how many of these committees:a particular student is included

There are 10 professors and 20 students out of whom a committee of 2 professors and 3 students is to be formed. Find the number of ways in which this can be done. Further, find in how many of these committees:
a particular student is included