In how many can a committee of 5 be formed from 4 professors and 6 students so as to include at least 2 professors ?

In how many ways can a committee of 6 members e formed out of 4 teachers and 7 students when (i) one teacher is in the committee? (ii) at least one teacher is in the committee?

In how many ways can a committee of 6 members e formed out of 4 teachers and 7 students when (i) one teacher is in the committee? (ii) at least one teacher is in the committee?

In how many ways a committee of 5 is to be formed from 6 boys and 4 girls, where the committee contains at least one girl.

There are 6 students A,B,C,D,E,F. In hoiw many ways can a committee of 4 be formed so as to always include C but exclude E?

There are 6 students A,B,C,D,E,F. In hoiw many ways can a committee of 4 be formed so as to always include C but exclude E?

In how many ways can a committee of four be selected from nine so as to always include a particular man?

Out of 6 gentlemen and 4 ladies a committee of 5 is to be formed. In how many ways can this be done so as to include at least one lady in each commiittee?

Out of 6 gentlemen and 4 ladies a committee of 5 is to be formed. In how many ways can this be done so as to include at least one lady in each commiittee?

From 8 gentlemen and 4 ladies a committee of 5 is to be formed. In how many ways can this be done so as to include at least one lady?

From 7 gentlemen and 4 ladies a committee of 5 is to formed. In how many ways can this be done so as to include at least one lady?