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Algebra II : Factorials

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Example Question #1 : Value Of E

What is the value of 5!+3 .

Possible Answers:

123

None of the other answers.

Correct answer:

123

Explanation:

When evaluating a factorial, you multiply the original number by each integer less than it, stopping at 1.

For this problem, this means that

$5! = 5\cdot 4\cdot 3\cdot 2\cdot 1 = 120$ .

Then adding 3, we get the answer 123

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Example Question #2 : Value Of E

Which of the following best represents the approximate value of e^3 ?

Possible Answers:

Correct answer:

Explanation:

The value of is defined as 2.71828 .

To find e^3 , simply cube the decimal number.

$e^3=2.71828\times 2.71828\times 2.71828 = 20.085$

The closest value of this number is:

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Example Question #1 : Factorials

Stewie has $\frac{5!}{3!}$ marbles in a bag. How many marbles does Stewie have?

Possible Answers:

1.66

Correct answer:

Explanation:

5!/3! = (5*4*3*2*1)/(3*2*1)

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

5!/3! = 5*4 = 20

Alternative Solution

5!/3! = (120/6) = 20

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Example Question #1 : Multiplying And Dividing Factorials

Which of the following is NOT the same as $\frac{6!\times5!}{4!}$ ?

Possible Answers:

$6\times5^{2}\times4!$

$\frac{6\times(5!)^2}{4!}$

$6\times5!$

$5\times6!$

$30\times5!$

Correct answer:

$6\times5!$

Explanation:

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

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Example Question #1 : Factorials

Simplify the following expression:

$\frac{7!(n+3)!}{6!(n+2)!}$

Possible Answers:

7!(n+3)

$\frac{n+3}{n+2}$

n+3

7n +3

7n + 21

Correct answer:

7n + 21

Explanation:

Recall that (n+3)! = (n+3)(n+2)(n+1)(n)... .

Likewise, $6! = 6\cdot 5\cdot 4\cdot 3\cdot 2\cdot 1$ .

Thus, the expression $\frac{7!(n+3)!}{6!(n+2)!}$ can be simplified in two parts:

$\frac{7!}{6!} = \frac{7\cdot 6\cdot 5\cdot 4\cdot 3\cdot 2\cdot 1}{6\cdot 5\cdot 4\cdot 3\cdot 2\cdot 1} = 7$

and

$\frac{(n+3)!}{(n+2)!} = \frac{(n+3)(n+2)(n+1...)}{(n+2)(n+1)...} = n+3$

The product of these two expressions is the final answer: 7n + 21

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Example Question #1 : Factorials

$\frac{6!}{2!4!} = ?$

Possible Answers:

$\frac{3}{4}$

Correct answer:

Explanation:

To simplify this, just write out each factorial:

$\frac{6!}{2!4!} = \frac{6*5*4*3*2*1}{(2*1)(4*3*2*1)} = \frac{6*5}{2*1} = 15$

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Example Question #5 : Multiplying And Dividing Factorials

Find the value of:

$\frac{7!}{3!}$

Possible Answers:

210

840

2.33

2520

Correct answer:

840

Explanation:

The factorial sign (!) just tells us to multiply that number by every integer that leads up to it. So, $\frac{7!}{3!}$ can also be written as:

$\frac{(7\times6\times5\times4\times3\times2\times1)}{(3\times2\times1)}$

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

$7\times6\times5\times4 = 840$

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Example Question #1 : Factorials

Which of the following is equivalent to $6!\times4!$ ?

Possible Answers:

None of the other answers are correct.

$(6!)^{2}-4!$

24!

10!

$30\times(4!)^2$

Correct answer:

$30\times(4!)^2$

Explanation:

This is a factorial question. The formula for factorials is $n! = n\times(n-1)\times(n-2)\times...\times1$ .

$6!=6\times5\times4! = 30\times 4!$

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Example Question #7 : Multiplying And Dividing Factorials

Divide 2015! by 2014!

Possible Answers:

3,870,890

4,058,210

2015

1,000,000

21,900,320

Correct answer:

2015

Explanation:

A factorial is a number which is the product of itself and all integers before it. For example $5!=5\cdot 4 \cdot 3 \cdot 2 \cdot 1$

In our case we are asked to divide 2015! by 2014! . To do this we will set up the following:

$\frac{2015!}{2014!}$

We know that 2015! can be rewritten as the product of itself and all integers before it or:

$2015!=2015 \cdot 2014!$

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

$\frac{2015 \cdot 2014!}{2014!}=2015$

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Example Question #8 : Multiplying And Dividing Factorials

$\frac{\left ( n+2\right )!}{n!}$

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

Possible Answers:

104

Correct answer:

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. $5\ast6=30$

So n would have to be 4 in this problem.

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Algebra II : Factorials

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #1 : Value Of E

Example Question #2 : Value Of E

Example Question #1 : Factorials

Example Question #1 : Multiplying And Dividing Factorials

Example Question #1 : Factorials

Example Question #1 : Factorials

Example Question #5 : Multiplying And Dividing Factorials

Example Question #1 : Factorials

Example Question #7 : Multiplying And Dividing Factorials

Example Question #8 : Multiplying And Dividing Factorials

All Algebra II Resources

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