Solved on Mar 18, 2024

Evaluate the expression $9! / 4!$ , where $n!$ represents the factorial of $n$ .

STEP 1

Assumptions
1. We need to calculate the value of the expression $\frac{9!}{4!}$ .
2. The notation $n!$ (n factorial) means the product of all positive integers from 1 to $n$ .

STEP 2

First, let's expand the factorials in the numerator and denominator to understand the expression better.
$9! = 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1$
$4! = 4 \times 3 \times 2 \times 1$

STEP 3

Now, we can write the expression with the expanded factorials.
$\frac{9!}{4!} = \frac{9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1}{4 \times 3 \times 2 \times 1}$

STEP 4

We can simplify the expression by canceling out the common factors in the numerator and the denominator.
$\frac{9!}{4!} = \frac{9 \times 8 \times 7 \times 6 \times 5 \times \cancel{4 \times 3 \times 2 \times 1}}{\cancel{4 \times 3 \times 2 \times 1}}$

STEP 5

After canceling out the common factors, we are left with:
$\frac{9!}{4!} = 9 \times 8 \times 7 \times 6 \times 5$

STEP 6

Now, we can multiply the remaining factors to find the value of the expression.
$\frac{9!}{4!} = 9 \times 8 \times 7 \times 6 \times 5 = 9 \times 8 \times 42 \times 5$

STEP 7

Continue the multiplication by combining numbers that are easy to multiply together.
$\frac{9!}{4!} = 72 \times 42 \times 5$

STEP 8

Multiply the remaining numbers.
$\frac{9!}{4!} = 3024 \times 5$

STEP 9

Finally, multiply 3024 by 5 to get the result.
$\frac{9!}{4!} = 3024 \times 5 = 15120$
The value of the expression $\frac{9!}{4!}$ is 15120.

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Evaluate the expression $9! / 4!$ , where $n!$ represents the factorial of $n$ .

STEP 1

Assumptions
1. We need to calculate the value of the expression $\frac{9!}{4!}$ .
2. The notation $n!$ (n factorial) means the product of all positive integers from 1 to $n$ .

STEP 2

First, let's expand the factorials in the numerator and denominator to understand the expression better.
$9! = 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1$
$4! = 4 \times 3 \times 2 \times 1$

STEP 3

Now, we can write the expression with the expanded factorials.
$\frac{9!}{4!} = \frac{9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1}{4 \times 3 \times 2 \times 1}$

STEP 4

We can simplify the expression by canceling out the common factors in the numerator and the denominator.
$\frac{9!}{4!} = \frac{9 \times 8 \times 7 \times 6 \times 5 \times \cancel{4 \times 3 \times 2 \times 1}}{\cancel{4 \times 3 \times 2 \times 1}}$

STEP 5

After canceling out the common factors, we are left with:
$\frac{9!}{4!} = 9 \times 8 \times 7 \times 6 \times 5$

STEP 6

Now, we can multiply the remaining factors to find the value of the expression.
$\frac{9!}{4!} = 9 \times 8 \times 7 \times 6 \times 5 = 9 \times 8 \times 42 \times 5$

STEP 7

Continue the multiplication by combining numbers that are easy to multiply together.
$\frac{9!}{4!} = 72 \times 42 \times 5$

STEP 8

Multiply the remaining numbers.
$\frac{9!}{4!} = 3024 \times 5$

STEP 9

Finally, multiply 3024 by 5 to get the result.
$\frac{9!}{4!} = 3024 \times 5 = 15120$
The value of the expression $\frac{9!}{4!}$ is 15120.

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Evaluate the expression 9!/4!9! / 4!9!/4!, where n!n!n! represents the factorial of nnn.

STEP 1

Assumptions1. We need to calculate the value of the expression 9!4! \frac{9!}{4!} 4!9!​.2. The notation n! n! n! (n factorial) means the product of all positive integers from 1 to n n n.

STEP 2

STEP 3

Now, we can write the expression with the expanded factorials.9!4!=9×8×7×6×5×4×3×2×14×3×2×1 \frac{9!}{4!} = \frac{9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1}{4 \times 3 \times 2 \times 1} 4!9!​=4×3×2×19×8×7×6×5×4×3×2×1​

STEP 4

STEP 5

After canceling out the common factors, we are left with:9!4!=9×8×7×6×5 \frac{9!}{4!} = 9 \times 8 \times 7 \times 6 \times 5 4!9!​=9×8×7×6×5

STEP 6

Now, we can multiply the remaining factors to find the value of the expression.9!4!=9×8×7×6×5=9×8×42×5 \frac{9!}{4!} = 9 \times 8 \times 7 \times 6 \times 5 = 9 \times 8 \times 42 \times 5 4!9!​=9×8×7×6×5=9×8×42×5

STEP 7

Continue the multiplication by combining numbers that are easy to multiply together.9!4!=72×42×5 \frac{9!}{4!} = 72 \times 42 \times 5 4!9!​=72×42×5

STEP 8

Multiply the remaining numbers.9!4!=3024×5 \frac{9!}{4!} = 3024 \times 5 4!9!​=3024×5

STEP 9

Finally, multiply 3024 by 5 to get the result.9!4!=3024×5=15120 \frac{9!}{4!} = 3024 \times 5 = 15120 4!9!​=3024×5=15120The value of the expression 9!4! \frac{9!}{4!} 4!9!​ is 15120.

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Evaluate the expression $9! / 4!$ , where $n!$ represents the factorial of $n$ .

Assumptions
1. We need to calculate the value of the expression $\frac{9!}{4!}$ .
2. The notation $n!$ (n factorial) means the product of all positive integers from 1 to $n$ .

Now, we can write the expression with the expanded factorials.
$\frac{9!}{4!} = \frac{9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1}{4 \times 3 \times 2 \times 1}$

After canceling out the common factors, we are left with:
$\frac{9!}{4!} = 9 \times 8 \times 7 \times 6 \times 5$

Now, we can multiply the remaining factors to find the value of the expression.
$\frac{9!}{4!} = 9 \times 8 \times 7 \times 6 \times 5 = 9 \times 8 \times 42 \times 5$

Continue the multiplication by combining numbers that are easy to multiply together.
$\frac{9!}{4!} = 72 \times 42 \times 5$

Multiply the remaining numbers.
$\frac{9!}{4!} = 3024 \times 5$

Finally, multiply 3024 by 5 to get the result.
$\frac{9!}{4!} = 3024 \times 5 = 15120$
The value of the expression $\frac{9!}{4!}$ is 15120.