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High School Math : Factorials

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Example Questions

Example Question #1 : Factorials

What is the value of ?

Possible Answers:

Correct answer:

Explanation:

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

Thus, 4! = 4 * 3 * 2 * 1 = 24 .

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Example Question #1 : Factorials

What is the value of ?

Possible Answers:

$\frac{1}{4}$

Correct answer:

Explanation:

By definition, $4! = 4 \cdot 3 \cdot 2 \cdot 1= 24$ .

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Example Question #1 : Factorials

Find the value of:

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

Possible Answers:

2.33

840

2520

210

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 : Multiplying And Dividing Factorials

Solve the following expression.

$\frac{10!}{8!}$

Possible Answers:

720

1.25

Correct answer:

Explanation:

$\frac{10!}{8!}=\frac{10*9*8*7*6*5*4*3*2*1}{8*7*6*5*4*3*2*1}$

This expression can be simplified because all terms in the expression for 8! are also found in the expression for 10!. By writing the expression below, we are able to cancel 8!.

$\frac{10*9*8!}{8!}=10*9=90$

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Example Question #2 : Multiplying And Dividing Factorials

Solve:

$\frac{10!}{7!}$

Possible Answers:

100

720

800

640

Correct answer:

720

Explanation:

Both the numerator and denominator are factorials. If you expanded both, everything would cancel out except for $10\cdot9\cdot8$ in the numerator. Multiply those together to get 720.

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Example Question #1 : Multiplying And Dividing Factorials

Simplify $\frac{ 8!}{6!}$ .

Possible Answers:

Correct answer:

Explanation:

8! = 8*7*6*5* . . . *2*1

6! = 6*5*4*3*2*1

Thus, $\frac{8!}{6!} = 8*7$ since the remaining terms cancel out. 56 is the simplified result.

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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:

$6\times5!$

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

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

$5\times6!$

$30\times5!$

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 #4 : Multiplying And Dividing Factorials

Simplify and solve $\frac{100!}{97!}$ .

Possible Answers:

9700

970,200

$7.5*10^{15}$

1.03

Correct answer:

970,200

Explanation:

Remember a number followed by a ! is a factorial. A factorial is the product of the given number and all of the numbers smaller than it down to zero. For example, 5!=5*4*3*2*1 .

Rather than do all of the math involved for 100! , notice that $\frac{100!}{97!}$ is the same as $\frac{100*99*98*97!}{97!}$

From here, the 97! 's cancel out, leaving us with 100*99*98=970,200 .

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Example Question #2 : Multiplying And Dividing Factorials

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

Possible Answers:

None of the other answers are correct.

24!

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

$30\times(4!)^2$

10!

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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High School Math : Factorials

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #1 : Factorials

Example Question #1 : Factorials

Example Question #1 : Factorials

Example Question #1 : Multiplying And Dividing Factorials

Example Question #2 : Multiplying And Dividing Factorials

Example Question #1 : Multiplying And Dividing Factorials

Example Question #1 : Factorials

Example Question #1 : Multiplying And Dividing Factorials

Example Question #4 : Multiplying And Dividing Factorials

Example Question #2 : Multiplying And Dividing Factorials

All High School Math Resources

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