A team of ten is to be formed from 6 male doctors and 10 nurses of whom 5 are male and 5 are female. In how many ways can this be done, if the team must have atleast 4 doctors and atleast 4 nurses with atleast 2 male nurses and at least 2 female nurses?

A committee of 10 is to be formed from 8 teachers and 12 students of whom 4 are girls. In how many ways this can be done so that com the committee contains atleast four of either groups (teachers and students) and atleast 2 girls and atleast 2 boys are in the committee.

A committee of 10 is to be formed from 8 teachers and 12 students of whom 4 are girls. In how many ways this can be done so that com the committee contains atleast four of either groups (teachers and students) and atleast 2 girls and atleast 2 boys are in the committee.

A committee of 11 is to be formed from 8 teachers and 12 students of whom 4 are girls. In how many ways this can be done so that the committee contains at least four of either groups (teachers and students) and at least 2 girls and atleast 2 boys are in the committee.

A committee of 7 has to be formed from 9 boys and 4 girls. In how many ways can this be done when the committee consists of: atleast 3 girls ?

A committee of 7 has to be formed 9 boys and 4 girls. In how many ways can this be done when the committee consists of : atleast 3 girls ?

If a team of four persons is to be selected from 8 males and 8 females, then in how many ways can the selections be made to include at least one male.