In a film institute there are 8 actors. and 4 directors. In how many ways Six can be choosen to include only one director

In how many ways a prizes can be given to one students of d batch A

In how many ways 5 letters can be posted in 4 letter boxes?

In a group of 15 boys there are 6 hockey players. In how many ways can 12 boys be selected so as to include at least 4 hockey players?

In how many ways can 4 letters be posted in 3 letter boxes?

In how many ways can 4 letters be posted in 5 letter boxes?

In how many ways can 4 letters be posted in 3 letter boxes?

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?

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?