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 excluded.

It is similar to selecting 2 professors and 3 students out of remaining 10 professors and 19 students as 1 student are already removed.

Let us assume the choosing the no. of ways be N₃,

⇒ N₃ = (choosing 2 professors out of 10 professors) × (choosing 3 students out of 19 students)

⇒ N₃ = ¹⁰C₂ × ¹⁹C₃

We know that

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

⇒

⇒ N₃ = 45 × 969

⇒ N₃ = 43605 ways.

∴ The required no. of ways are 51300, 10260, 7695, 43605.

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 excluded.

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 excluded.