A committee of 5 is to be formed out of 6 gents and 4 ladies. In how many ways can be done when each committee may have at the most two ladies?

A committee of 5 members is to be formed out of 4 men ad 5 women. In how many ways this can be done.

A committee of 5 persons is to be formed from a group of 6 gentleman and 4 ladies. In how many ways can this be done if the committee is to include at least one lady ?

A committee of 5 is to be formed out of 6 men and 4 ladies. In how many ways can this be done, when (a) at least 2 ladies are included, (b) at most 2 ladies are included?

A committee of 5 is to be formed out of 6 men and 4 ladies. In how many ways can this be done, when (a) at least 2 ladies are included, (b) at most 2 ladies are included?

A committee of 6 is to be formed from 6 men and 4 women. In how many ways can this be done if the committee contains at least 2 women?

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 at most 3 girls.