1. How many ways can a committee of 4 people be selected from a group of 8 people?

2. Find the number of ways of selecting a captain and a vice-captain from a team of 11 players.

3. In the card game of Poker how many hands of 5 cards can be dealt from a normal pack of 52 cards?

4. Find the number of ways in which a group of 9 people can be split into two groups, one containing 4 people and the other containing 5 people.

5. Find the number of ways in which you could select a committee of 5 from a group of 8 men and 7 women if there must not be less than two members of either sex on the committee.

6. A mixed team of 4 players is to be chosen from a group of 5 boys and 6 girls.

(i) If the team can contain any numbers of boys and girls how many different teams could be chosen?

(ii) If the only restrictions on the team were that one particular boy and one particular girl had to be chosen, how many different teams could be picked?

(iii) If the team had to contain two girls and two boys, how many teams could be chosen?