# Algebra II : Multiplying and Dividing Factorials

## Example Questions

### Example Question #1 : Factorials

Stewie has   marbles in a bag. How many marbles does Stewie have?

Explanation:

Simplifying this equation we notice that the 3's, 2's, and 1's cancel so

Alternative Solution

### Example Question #1 : Multiplying And Dividing Factorials

Which of the following is NOT the same as ?

Explanation:

The  cancels out all of  except for the parts higher than 4, this leaves a 6 and a 5 left to multilpy

### Example Question #1 : Factorials

Simplify the following expression:

Explanation:

Recall that .

Likewise, .

Thus, the expression  can be simplified in two parts:

and

The product of these two expressions is the final answer:

### Example Question #1 : Multiplying And Dividing Factorials

Explanation:

To simplify this, just write out each factorial:

### Example Question #5 : Multiplying And Dividing Factorials

Find the value of:

Explanation:

The factorial sign (!) just tells us to multiply that number by every integer that leads up to it.  So,  can also be written as:

To make this easier for ourselves, we can cancel out the numbers that appear on both the top and bottom:

### Example Question #1 : Multiplying And Dividing Factorials

Which of the following is equivalent to ?

None of the other answers are correct.

Explanation:

This is a factorial question. The formula for factorials is .

### Example Question #7 : Multiplying And Dividing Factorials

Divide  by

Explanation:

A factorial is a number which is the product of itself and all integers before it. For example

In our case we are asked to divide  by . To do this we will set up the following:

We know that  can be rewritten as the product of itself and all integers before it or:

Substituting this equivalency in and simplifying the term, we get:

### Example Question #8 : Multiplying And Dividing Factorials

If  is a postive integer, which of the following answer choices is a possible value for the expression.

Explanation:

This expression of factorials reduces to (n+1)(n+2).  Therefore, the solution must be a number that multiplies to 2 consecutive integers.  Only 30 is a product of 2 consecutive integers.

So n would have to be 4 in this problem.

### Example Question #9 : Multiplying And Dividing Factorials

Simplify:

Explanation:

Remember what a factorial is, and first write out what the original equation means. A factorial is a number that you multiply by all whole numbers that come before it until you reach one.

You can simplify because all terms in the expression 17! are found in 20!.

Thus:

Simplify: