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 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 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.

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 ?

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 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 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?

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 ?

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

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 ?