Permutations 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? Letters A AB ABCDE Arrangements number

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.