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?

Out of 7 men and 4 ladies committee of 5 is to be formed. In how many ways can this be done so as to include at least 3 ladies?

From 6 gentlemen and 4 ladies a committee of 5 is to be formed. In how many ways can this be done if,( i). there is no restriction (ii). the committee is to include at least one lady.

Out of 5 men and 2 women, a committee of 3 is to be formed. In how many ways can it be formed if at least one woman is to be included?

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 6 is to be formed out of 4 boys and 6 girls. In how many ways can it be done so that the girls may not be out numbered?

A commttee of 8 is to be formed from 6 women and 5 men. In how many ways this can be done if men are in majority ?

A committee of 4 is to be selected from amongest 5 boys and 6 girls . In how many ways can this be done so as to include (i) exacity one girls ,(ii) at least one girl?

A committee of 12 is to be formed from nine women and eight men. In how many ways can this be done if at least five women have to be included in a committee? In how many of these committees a. the women hold majority? b. the men hold majority?

There are 5 gentlemen and 4 ladies to dine at a round table. In how many ways can they as themselves so that no that ladies are together ?