Counting Methods – Part 2 Determine the number of ways of getting a sequence of events.

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Presentation transcript:

Counting Methods – Part 2 Determine the number of ways of getting a sequence of events.

Permutation An arrangement of people or objects

For example: A bowling club consists of 8 members, from which a president, a vice president, and a treasurer are selected. This is called a permutation of 3 items from 8 available items.

To calculate n P r

What is the value of 7 P 2 ?

What is the value of 30 P 30 ? Don’t forget that 0! = 1

Summary of formulas and special cases:

Math Flash!!! 7 P 3 means to begin with 7 and multiply 3 numbers, counting down by ones from 7. 7 P 3 =7x6x5 To calculate the last number by (7-3+1)=5. So we know that the last number is 5

In how many different ways can all the letters of the word “CITY” be arranged to form a sequence of 4 letters? 4!

In how many different ways can all the letters of the word “BROOM” be arranged to form a sequence of 5 letters? Be careful!!! The answer is not 5! The sequence BRO 1 O 2 M would appear the same as the sequence BRO 2 O 1 M. Likewise, BO 1 RO 2 M or BO 2 RO 1 M The way to handle this situation is to pretend that the word “BROOM” has 5 different letters and then divide by 2!.

In how many different ways can all the letters of the word “BANANA” be arranged?

In how many different ways can all the letters of the word “MISSISSIPPI” be arranged?