Q. 5 B5.0( 2 Votes )
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
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
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