Permutation- an arrangement of a set of distinct objects in a certain order. Ex. Set of objects { A, B, C, D} ABCD BACD DCBA BCAD Each of these is a permutation.

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Presentation transcript:

Permutation- an arrangement of a set of distinct objects in a certain order. Ex. Set of objects { A, B, C, D} ABCD BACD DCBA BCAD Each of these is a permutation of the set { A, B, C, D}. How many permutations of the set are possible? If you have n objects, the number of possible permutations is n! *Note: Permutations can be found using The Counting Principle

A permutation is not always arranging all of the items in the given group. Ex. Use the 10 digits to make a 4 digit code with no repetition of digits. Counting Principle - 10 * 9 * 8 * 7 = 5040 OR Permutation Formula: n- is the number of items you have. r- is the number of items you are arranging.

Counting Principle - 10 * 9 * 8 * 7 = 5040 Permutation Formula:

Use the n P r button when n and r are large otherwise the Counting Principle is just as easy. Ex. You have 115 pictures to place in a photo album. The album has 20 pages. Each page hold one picture. In how many ways can the album be filled?

If the items to be arranged are not all unique, we need to account for the repeats. Ex. Find the number of unique arrangements for the word honk and hook. Honk has 24 possible arrangements. Hook has only 12 because ever ytime the o’s switch around the word still looks the same. (There are 2! ways to arrange 2 letters.) Given n objects with a alike and b alike, the number of distinguishable permutations of the n objects is:

Permutations with repetitions is also called finding the number of partitions. Ex. A group of 10 students is assigned to complete cleaning tasks around the school during detention. Five are needed to clean desks, 3 to paint parking bumbers, and 2 to pick up trash in the locker tunnel and lunch area. In how many ways can the students be assigned the cleaning duties? Hint: 10 jobs of which, 5 are the same, 3 others are the same and the final 2 are the same. Do this just like the repeated letters. End here for viewing guide.

Beth, Jill, Angel, and Lenny found 4 seats together at a crowded theater. If Jill insists on sitting next to Lenny, in how many ways can they be seated? Practice #13 worksheet and p all