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 a particular is always included.

It is similar to selecting 1 professor and 3 students out of the remaining 9 professors and 20 students as 1 professor is already selected.

Let us assume the choosing the no. of ways be N₁,

⇒ N₁ = (choosing 1 professor out of 9 professors) × (choosing 3 students out of 20 students)

⇒ N₁ = ⁹C₁ × ²⁰C₃

We know that

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

⇒

⇒ N₁ = 9 × 1140 ways

⇒ N₁ = 10260 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 professor 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 professor is included