12.5 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
3
c
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
11
c 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
9
c 4
=126