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Unordered arrangements (Combinations) Therefore there are 6 different pairs. Permutations looked at ordered arrangements, eg how many trifectas are there in a 10 horse race? 10 P 3 = 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. 720 =120

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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 In general, the number of unordered selections you can make from n items if r of the items are used is given by: = 120 This line is the number of ways you can select 3 horses from 10. This line is the number of ways you can arrange the 3 horses.

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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

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Example 2 A student council must elect 8 junior members and 4 senior members. There are 25 junior candidates and 11 senior candidates. a)How many different ways can the 8 junior members be selected? b)How many different ways can the 4 senior members be selected? c)Hence, how many different student councils are possible? 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.

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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. 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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Today’s work Exercise 7E Page 219 Q3, 5, 7, 9, 11, 13, 15

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