Permutations and Combinations

Permutations and Combinations

Elizabeth Borres

Multiple Choice

How many ways can you arrange 7 books on a shelf?

• 7

• 49

• 343

• 5,040

Multiple Choice

There are 18 people running in a cross country race. How many possible ways are there to place the runners in first, second, and third?

• 324

• 4,896

• 816

• 54

Multiple Choice

Sarah plays softball over the summer.  If there are 10 players on the team, how many ways can the coach make a batting order that includes all players?

• 1
• 3628800
• 100
• 1814400

Objectives:

1. Review permutations.

2. Define Combination.

3. Find the combinations of things.

What Is Combination In Math?

• An arrangement of objects in which the order is not important is called a combination.

• This is different from permutation where the order matters.

Example

• For example, suppose we are arranging the letters A, B and C.

• In a permutation, the arrangement ABC and ACB are different.

• But, in a combination, the arrangements ABC and ACB are the same because the order is not important.

How To Use The Combination Formula To Solve Word Problems?

• In how many ways can a coach choose three swimmers from among five swimmers?

• There are 5 swimmers to be taken 3 at a time.

• The coach can choose the swimmers in 10 ways.

Six friends want to play enough games of chess to be sure every one plays everyone else. How many games will they have to play?

• There are 6 players to be taken 2 at a time.

• They will need to play 15 games.