1. Mixed arrangements There are five different ways to systematically determine the number of outcomes in a multi stage event: * Write a list of all possibilities and count them. * Draw a tree diagram to help you systematically list all possibilities * Multiply the number of possibilities at each stage of the multistage event. * Use ‘combinations’ and the n C r button when choosing part of the group and order is not important. * Use ‘permutations’ and the n P r button when choosing part of the group and order is important.

2. Mixed arrangements You must be able to distinguish between permutations and combinations. Permutations are ordered arrangements. Here the order within the group is imPortant. Here ABC, ACB and CBA are considered different arrangements. Examples include: Picking a trifecta in a 10 horse race. Picking president and secretary from a group of 6 people. Combinations are unordered selections. Here the order within the group is not important (or who Cares). Here ABC, ACB and CBA are considered the same. Examples include: Picking 3 horses in a 10 horse race. Picking a committee of 2 from a group of 6 people.

3. Example 1 In the “pools” you need to pick 6 numbers from 38. In the strike version of the game you need to pick the first 4 balls in the order in which they come out of the container. a) How many different ways are there of selecting the 6 balls? b) How many different strike games could you play? c) In a system 8 you pick from only 8 numbers. How many different combinations of 6 numbers is this? d) If Sarah plays a system 8, what is the probability that she wins? a)2 760 681 38 C 6 = b)1 771 560 38 P 4 = c)28 8C6 =8C6 = d)P(win with system 8) = This is about 1 in 98 600

4. Example 2 In poker you are dealt a hand of 5 cards. a)How many different hands are possible? b)How many ways can you pick 3 kings from the 4 in the deck? c)How many ways can you pick 2 jacks from the 4 in the deck? d)What is the probability of being dealt 3 kings and 2 jacks? e)How many ways can you pick 5 cards from the same suit? f)A flush is 5 cards from the same suit. What is the probability of being dealt a flush in hearts? g)What is the probability of being dealt a flush? a)2 598 960 52 C 5 = b)4 4C3 =4C3 = c)6 4C2 =4C2 = d)4 × 6 =Ways of selecting 3K & 2J =24 P(3K, 2J) = e)1287 13 C 5 = P(Flush H) =f) P(Flush) =g) Times by 4 as there are 4 suits

5. × 5! = × 3! = Example 3 Kathini has 4 english books and 2 maths books. a)How many ways can the books be arranged on the shelf ? b)How many ways are the 4 english books together? c)What is the probability the maths books are together? a)7206! = b)1444! c)2402! now there are 3 groups of books 1 english and 2 maths P(maths together) = 4 english books, How many ways can the maths books be together? now there are 5 groups of books 4 english and 1 maths 2 maths books,

6. Today’s work Permutations and Combinations Worksheets