# Algebra II : Algebra II

## Example Questions

### Example Question #7 : 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?

Explanation:

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

### Example Question #1 : Permutations

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

Explanation:

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.

### Example Question #11 : Permutations

The soccer team awards gold, silver, and bronze trophies for the top three goal scorers over the season. If the soccer team has 11 players, how many different ways could the gold, silver, and bronze trophies be awarded?

Explanation:

Because the order is important, this is a permutation. There are 11 players to fill 3 spots, so .

### Example Question #51 : Probability

How many possible ways can the letters A and B be assigned to nine people?

Explanation:

Write the formula for permutation.

Evaluate .

Cancel all the common terms in the numerator and denominator.

### Example Question #53 : Probability

Evaluate:

Explanation:

Write the permutation formula.

Substitute the values in the given problem.

Cancel out the terms in the numerator and denominator.

The remaining terms in the numerator are:

### Example Question #11 : Permutations

Evaluate:

Explanation:

Write the permutation formula.

Substitute the values of the variables.

Simplify the factorials.

Cancel the common terms.

### Example Question #55 : Probability

Determine the value of:

Explanation:

Write the permutation formula.

Substitute the values of  into the formula.

Expand the terms.

Cancel out the terms in the denominator and denominator.

The remaining terms are:

Multiply these numbers.

### Example Question #56 : Probability

Solve the permutation:

Explanation:

Write the formula for permutation.

Substitute the values and expand the factorials.

Reduce the terms.

### Example Question #51 : Probability

Suppose a locksmith designs a three digit lock with numbers ranging only from zero to five.  What is the number of permutations possible?

Explanation:

The formula to determine the permutation is:

Notice that for each number, there are 6 different choices since we have numbers ranging from zero to five, not five.

For a three digit lock, .

Substitute the terms into the formula.

### Example Question #11 : Permutations

There are  runners in a race. How many different arrangements are there for , , and  place?