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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:

有限公司rrect 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 #1433 :High School Math

What is the value of?

Possible Answers:

$\frac{1}{4}$

有限公司rrect answer:

Explanation:

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

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Example Question #1 :乘法、除法阶乘

Find the value of:

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

Possible Answers:

2.33

840

2520

210

有限公司rrect answer:

840

Explanation:

The factorial sign (!) just tells us to multiply that number by every integer that leads up to it. So, $\frac{7!}{3!}$ 也可以写成:

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

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 #2 :Factorials

Solve the following expression.

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

Possible Answers:

1.25

720

有限公司rrect 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 #1 :乘法、除法阶乘

Solve:

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

Possible Answers:

640

800

720

100

有限公司rrect 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 :乘法、除法阶乘

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

Possible Answers:

有限公司rrect 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 :乘法、除法阶乘

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

Possible Answers:

1.66

有限公司rrect 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 #5 :乘法、除法阶乘

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

Possible Answers:

$6\times5!$

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

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

$30\times5!$

$5\times6!$

有限公司rrect answer:

$6\times5!$

Explanation:

Thecancels out all ofexcept for the parts higher than 4, this leaves a 6 and a 5 left to multilpy

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Example Question #6 :乘法、除法阶乘

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

Possible Answers:

970,200

1.03

$7.5*10^{15}$

9700

有限公司rrect 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 #1 :乘法、除法阶乘

哪个following is equivalent to $6!\times4!$ ?

Possible Answers:

10!

$30\times(4!)^2$

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

24!

None of the other answers are correct.

有限公司rrect 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 #1433 :High School Math

Example Question #1 :乘法、除法阶乘

Example Question #2 :Factorials

Example Question #1 :乘法、除法阶乘

Example Question #1 :乘法、除法阶乘

Example Question #1 :乘法、除法阶乘

Example Question #5 :乘法、除法阶乘

Example Question #6 :乘法、除法阶乘

Example Question #1 :乘法、除法阶乘

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