If there are n 1 objects of one kind and n 2 of

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If there are n 1 objects of one kind and n 2 of another, then there are n 1 × n 2 ways of selecting both. That is, total number of outcomes = n 1 × n 2 In general if there are k groups of objects, and there are n 1 items in the first group, n 2 items in the second, …, and n k items in the k th group, the number of ways we can select one item each from the k groups is: n 1 × n 2 × …….. × n k If n 1 = n 2 = …….. = n k , then n 1 × n 2 × …….. × n k = n k Slide 33
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Example 5 Dr. Asempa has 10 shirts and 8 ties. How many shirt/tie outfits does he have? Answer = 10x8 = 80. Slide 34
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Permutation formula The permutation formula is applied to find the number of outcomes when there is only one group. We are interested in how many different subsets that can be obtained from a given set of objects. Example - the number of ways of having 3 girls in a family of 5 children. If r items are selected from a set on n objects (where r n ), any particular sequence of these r items is called a permutation. Slide 35
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Permutation formula The formula is Where n = total number of objects r = number of objects selected at a time n! is called “n factorial” and it is the product of all the positive integers up to and including n. Slide 36 ! ! n n P r n r 1 ) 2 ( ) 1 ( ! n n n n
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Permutation So the number of different ways of having 3 girls in a family of 5 children is In permutation the order of arrangement of the objects is important! For example, the arrangement (Kofi, Ama) is a different permutation from (Ama, Kofi) even though it is the same two individuals. Slide 37 5 4 3 2 1 5 3 60 2 1 P
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