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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