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There are 5 professors and 6 students out of whom a committee of 2 professors and 3 students is to be formed such that a particular student is excluded.

(a) 100 

(b) 150 

(c) 200 

(d) 125

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(a) 100

If a particular student is excluded, then the committee has to be chosen as: 2 professors from 5 professors and 3 students from 5 students (as one student is excluded) 

∴ Total number of ways of forming the committee 

= 5C2 × 5C3 

= \(\frac{5!}{2!3!}\times\frac{5!}{3!2!}\) 

= \(\frac{5\times4}{2}\) x \(\frac{5\times4}{2}\) = 100.

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