How many ways a captain and a vice-captain can be selected from a team of 11 players?

In how many ways a committee, consisting of 5 men and 6 women can be formed from 8 men and 10 women?

From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. In how many ways can it be done?

How many words can be formed from the letters of the word 'ENGINEER'?

In a group of 6 boys and 4 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be there?

If a cube is to be painted with red and blue colour in such a way that each face gets exactly one colour, then in how many ways this cube can be painted?