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15.4 Permutations with Repetition
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How many different ways can the letters of MEXICO be arranged?
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How is this different than MEXICO? How many different ways can the letters of CANADA be arranged? CANADACANADA
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Look at the options for the arrangement NADACA NADACANADACANADACANADACANADACANADACANADACANADACANADACANADACANADACANADACA Are these different? When you take the permutation are all of these counted? Should they be?
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The Number of Permutations of Things Not All Different Let S be a set of n elements of k different types. Let n 1 = the number of elements of type 1, n 2 = the number of elements of type 2, …, n k = the number of elements of type k. Then the number of distinguishable permutations of the n elements is:
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So back to CANADA How many of each type of letter is there? A – 3 C – 1N – 1D – 1
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How many permutations are there of MISSISSIPPI?
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Exit Ticket A teacher’s grade book alphabetically lists 25 students in a class. This teacher, who does not give pluses and minuses with letter grades, announces that on the last test there were: 5 A’s, 10 B’s, 6 C’s, 3 D’s and 1 E. In how many ways can these grades be distributed to the 25 students? And write your name. HW: p. 580, 1 – 13 odd.
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