Unordered arrangements (Combinations)

1
Unordered arrangements (Combinations)
Permutations looked at ordered arrangements, eg
how many trifectas are there in a 10 horse race?
10P3
720
Combinations look at unordered arrangements, eg
how many groups of 3 horses can you pick from 10
horses? The difference can be seen by how many
pairs of jellybeans can be selected from a Blue,
Green, Pink Red jellybean. BG BP
BR GB GP GR PB PG
PR RB RG RP Here there are 12
(4 3) ordered arrangements. BUT if we are just
after pairs, there are double ups. Eg, BG and GB
are the same event.
120
Therefore there are 6 different pairs.
2
Unordered arrangements (Combinations)
To work out (without combinations) how many
groups of 3 horses can you pick from 10 horses,
you would do
10 9 8 3 2 1
120
In general, the number of unordered selections
you can make from n items if r of the items are
used is given by
3
Example 1
In lotto 6 balls are randomly selected from
44. How many different ways are there of
selecting the balls?
There are 44 balls and 6 positions
Number of possible selections
7,059,052
4
a)
1,081,575
b)
330
c) Number of possible student councils
1,081,575 330 356,919,750
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Example 3
Immy has 5 friends (Oliver, Becky, April, Yvette
and Gertrude) but she can only choose three to be
her bridesmaids. Make a list of the different
possible bridesmaid selections she can make.

6
Example 3
Immy has 5 friends (Oliver, Becky, April, Yvette
and Gertrude) but she can only choose three to be
her bridesmaids. Make a list of the different
possible bridesmaid selections she can make.
Oliver, Becky, April Oliver, Becky,
Yvette Oliver, Becky, Gertrude Oliver, April,
Yvette, Oliver, April, Gertrude Oliver, Yvette,
Gertrude Becky, April, Yvette Becky, April,
Gertrude Becky, Yvette, Gertrude April, Yvette,
Gertrude
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Todays work
Exercise 7E Page 219 Q3, 5, 7, 9, 11, 13, 15