From 4 officers and 8 jawans in how many ways can 6 be chose To include exactly one officer To include at least one officer?

From 4 officers and 8 clerks, in how many ways can 6 be chosen (i) to include exactly one officer, (ii) to include at least one officer?

From 4 officers and 8 jawans, a committee of 6 is to be chosen to include exactly one officer. The number of such committees is :

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.

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 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 ?