### All Algebra II Resources

## Example Questions

### Example Question #1 : Permutations

Find the Computing Permutation.

**Possible Answers:**

**Correct answer:**

### Example Question #1 : How To Find The Number Of Integers Between Two Other Integers

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?

**Possible Answers:**

**Correct answer:**

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 #2 : How To Find The Missing Number In A Set

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

- President
- Vice President
- Secretary
- Treasurer

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

How many ways the executive body can be formed?

**Possible Answers:**

**Correct answer:**

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 #2 : Permutations

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

**Possible Answers:**

None of the above

**Correct answer:**

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?

**Possible Answers:**

**Correct answer:**

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 #4 : Permutations

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

**Possible Answers:**

**Correct answer:**

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 #5 : Permutations

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

**Possible Answers:**

**Correct answer:**

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?

**Possible Answers:**

**Correct answer:**

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

### Example Question #6 : 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?

**Possible Answers:**

**Correct answer:**

There are 7 potential actors and 2 different roles to fill. This would be calculated as divided by , or 42

### Example Question #2 : Permutations

How many different 4 letter words can be made out of the letters A, B, C, D, and E?

**Possible Answers:**

**Correct answer:**

Since order matters, use the permutation formula:

There are 5 letters to choose from (n), and you pick 4 of them (r).

So there are 120 possible words that can be formed.

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