Permutations & Combinations

Counting Principle

If there are 3 meats, 5 vegetables, and 2 types of bread to choose from for a meal, how many different meals are possible?

How many answer keys are possible for a 5 question true/false quiz?

How many 7-digit phone numbers are possible?

If a license plate has 3 letters followed by 3 numbers, how many plates are possible?

How many ways can I read six magazines out of 10?

Permutation – order is important

Suppose that a club with 12 members wishes to choose a president, a vice-president, and a treasurer.

The order is important. How many ways can this be done?

Can you develop a formula for finding a permutation?

Let’s check to see if you’re right:

!

( )!n r

nP

n r

Combination – order doesn’t matter

Suppose the club merely wants to choose a governing council of 3.

Now for each governing council of 3 that can be chosen (say A, B, C) there are ____ different slates of officers. In other words they are the same.

So how many governing councils are there?

Can you develop a formula for Combinations?

Let’s check to see if you’re right!

!

( )! !n r

nC

n r r

I want to take three books out of my collection of 10 to school to put on my desk. How many ways can this be done?

A company advertises two job openings for computer programmers, both with the same salary and job description. In how many ways can the openings be filled if 8 people apply?

A company advertises two job openings, one for a copywriter and one for an artist. If 10 people who are qualified for either position apply, in how many ways can the openings be filled?

For a certain raffle, 845 tickets are sold. In how many ways can four $50 gift certificates be awarded?

How many ways can a $100, a $50, a $20, and a $10 gift certificate be awarded?

Permutations & Combinations can be done on the graphing calculator! Type the n (# of items) Press math, Prb Choose the appropriate key (#2 or #3) Type the r (# chosen) Press enter

How many ways can I choose six people for a committee in a class of 20?

How many ways can I select four bikes from seven?

At the Red Lion Diner, an omelet can be ordered plain or with any or all of the following fillings: cheese, onions, peppers. How many different kinds of omelets are possible?

There are 8 different kinds of cookies and 11 different cakes. How many ways can I choose 3 types of cookies and 5 different cakes?

There are 10 different magazines and 12 different books. How many ways can I choose 3 if I want at most 2 books?

How many permutations are in the word letter?

How many permutations are in the word Mississippi?

Homework

Worksheet