# Algebra II : Other Factorials

## Example Questions

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### Example Question #1 : Understanding Factorials

What is the value of  ?

6

12

4

24

10

24

Explanation:

! is the symbol for factorial, which means the product of the whole numbers less than the given number.

Thus,

### Example Question #1 : Other Factorials

What is the value of ?

None of the other answers are correct.

Explanation:

Since the factorial has the property

we can write  as:

.

Thus, our expression can be written as

### Example Question #2 : Other Factorials

What is the value of  ?

Explanation:

A factorial represents the product of all natural numbers less than a given number. Thus,  which gives us

### Example Question #3 : Other Factorials

Explanation:

First, move all terms to the left by subtracting the quantity on the right.

From here, factor the quadractic into two binomials and set each equal to zero.

### Example Question #4 : Other Factorials

What is ?

Explanation:

Remember that factorial is defined as:

So using this definition,

And

So

The 7, 6, 5, 4, 3, 2, and 1 all cancel from both the numerator and denominator. So we're left with just  on top, which has a value of .

### Example Question #5 : Other Factorials

How many -permutations (without repetition) are there when taking numbers from the set of numbers ?

Explanation:

The elements of the set don't matter. Only the size of the set matters when determining permutations.

Our set contains 9 integers, so for the first number in our permutation, we have 9 choices.

After picking that number, because we're not allowed repetition, our second number is from 8 choices.

Our final number is from 7 choices.

Multiplying  gives us .

### Example Question #6 : Other Factorials

What can   be expressed as?

Explanation:

A factorial means you are multiplying the number, with one less than previous number and you keep multiplying until you reach . Since we are dealing with variables, let's analyze them.  is definitely greater than  in this situation because factorials are always positive numbers. If we took the difference between  and  we would get . This means after , the next biggest value is . Since we have  and the next value multiplied is , we can conclude that  will work since it incorporates  values multiplied and also .

### Example Question #7 : Other Factorials

What is ?

Explanation:

A factorial means you are multiplying the number, with one less than previous number and you keep multiplying until you reach .

So,  is .

Multiplying that out, we get

### Example Question #8 : Other Factorials

What is ?

Explanation:

A factorial means you are multiplying the number, with one less than previous number and you keep multiplying until you reach

So,  is .

Multiplying that out, we get

### Example Question #9 : Other Factorials

What is ?

Explanation:

A factorial means you are multiplying the number, with one less than previous number and you keep multiplying until you reach

So,  is . Multiplying that out, we get .

We also have . That is  or .

Since we are multiplying the factorial, we multiply  and  to get

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