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.


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