1. 15.4 Permutations with Repetition

2. How many different ways can the letters of MEXICO be arranged?

3. How is this different than MEXICO? How many different ways can the letters of CANADA be arranged? CANADACANADA

4. 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?

5. 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:

6. So back to CANADA How many of each type of letter is there? A – 3 C – 1N – 1D – 1

7. How many permutations are there of MISSISSIPPI?

8. 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.