(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.