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


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