# Algebra II : Permutations

## Example Questions

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### Example Question #1 : Permutations

Find the Computing Permutation.

Explanation:

### Example Question #2 : Permutations

An ice cream vendor sells five different flavors of ice cream.

In how many ways can you choose three scoops of different ice cream flavors if order matters?

Explanation:

There are five ways to choose the first scoop, then four ways to choose the second scoop, and finally three ways to choose the third scoop:

5 * 4 * 3 = 60

### Example Question #1 : Permutations

There are 5 men and 4 women competing for an executive body consisting of :

1. President
2. Vice President
3. Secretary
4. Treasurer

It is required that 2 women and 2 men must be selected

How many ways the executive body can be formed?

Explanation:

2 men can be selected:

2 women can be selected out of 4 women:

Finally, after the selection process, these men and women can fill the executive body in ways.

This gives us a total of

### Example Question #4 : Permutations

There are 10 runners in a race. How many different arrangements are there for 1st, 2nd, and 3rd place?

Explanation:

This is a permutation of 10 objects (runners) taken 3 at a time, with no replacements.

Another way to look at this would be there are 10 runners competing for 1st place, 9 runners competing for 2nd place, and 8 runners competing for 3rd place.

### Example Question #2 : Permutations

How many ways can a three committee board select the president, vice president and treasurer from a group of 15 people?

None of the above

Explanation:

In this problem, order is important because once someone is chosen as a position they can not be chosen again, and once a position is filled, no one else can fill that in mind.

The presidential spot has a possibility of 15 choices, then 14 choices for vice president and 13 for the treasurer.

So:

### Example Question #3 : Permutations

How many ways can you re-arrange the letters of the word JUBILEE?

Explanation:

There are 7 letters in the word jubilee, so initially we can calculate that there are ways to re-arrange those letters. However, The letter e appears twice, so we're double counting. Divide by 2 factorial (2) to get .

### Example Question #7 : Permutations

How many ways can you re-arrange the letters of the word BANANA?

Explanation:

At first, it makes sense that there are ways to re-arrange these letters. However, the letter A appears 3 times and the letter N appears twice, so divide first by 3 factorial and then 2 factorial:

### Example Question #4 : Permutations

In a class of 24 students, how many distinct groups of 4 can be formed?

Explanation:

To solve, evaluate

### Example Question #5 : Permutations

13 rubber ducks are competing in a race. How many different arrangements of first, second, and third place are possible?

Explanation:

There are 3 winners out of the total set of 13. That means we're calculating

### Example Question #10 : Permutations

7 students try out for the roles of Starsky and Hutch in a new school production. How many different ways can these roles be cast?