Combinations Practical Applications When we hear about committees or when a question says ‘how many different ways’ we use combinations Think about people standing on one side of a room and the ones we want have to walk over to the other side e.g 1 How many ways can a committee of 5 people be chosen from a group of 8 8 c 5 =56

e.g 2 How many ways can 3 books be chosen from a shelve of 10 =120

e.g 2 How many ways can a team of 5 players be chosen from a squad of 11 (i) if there are no restrictions (ii) If a certain member must be on the team (iii) If a certain player cannot play (iv) If one player cannot player and one must play c 11 5 =462

e.g 2 How many ways can a team of 5 players be chosen from a squad of 11 (ii) If a certain member must be on the team 4 c 10 =210

e.g 2 How many ways can a team of 5 players be chosen from a squad of 11 (iii) If a certain player cannot play 5 c 10 =120

e.g 2 How many ways can a team of 5 players be chosen from a squad of 11 (iv) If one player cannot player and one must play 4 c 9 =126