Lesson 4.6! Part 1: Factorial Notation!

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Presentation transcript:

Lesson 4.6! Part 1: Factorial Notation! Permutations! Lesson 4.6! Part 1: Factorial Notation!

Permutation A permutation is an ordered arrangement of objects selected from a set. The ORDER of the events is IMPORTANT.

Using the letters given below, how many arrangements are possible? number Letters A AB ABC ABCD ABCDE Arrangements

Factorial Notation! We often want to be able to count the permutations of a list of objects. As you can see, the pattern of multiplying “descending” numbers occurs frequently…. It happens so much, there is a special notation and name for this

n-factorial or n! The general form of factorial is

Working with Factorial Factorial has some nice properties.

Working with Factorial You can expand it as far as you need to…

Example 1: Simplify a) b) c) n(n-1)! = d)

Permutations when all objects are selected. Ex. #2: How many different ways can 7 students line up for a class photo? Ex. #3: How many different permutations are there for the letters in the word OPEN?

Permutations with less elements Suppose we want to know how many four letter words (maybe nonsensical) can be formed with the six letters ABCDEF. Here we want to calculate “six permute four” Ex #4: There are 12 players on the school baseball team. How many ways can the coach complete the 9 person batting order?

Permutation Notation P(n,r) represents the number of permutations possible, in which r objects from a set of n different objects are arranged. This can also be written as

Ex #5: Working with factorial P(6,4)= P(10,2)= P(12,9)=

Practice Questions! Page 239 #1-4, 6, 7.