Question Calculate the exact value of the ${ }_{27} P_{4}$ permutation expression.

Studdy Solution

STEP 1

Assumptions
1. The expression ${ }_{27} P_{4}$ represents the number of permutations of 27 distinct items taken 4 at a time.
2. The formula for permutations is given by ${ }_{n} P_{k} = \frac{n!}{(n-k)!}$ , where $n$ is the total number of items and $k$ is the number of items to be arranged.

STEP 2

We will use the permutation formula to calculate the value of ${ }_{27} P_{4}$ .
${ }_{27} P_{4} = \frac{27!}{(27-4)!}$

STEP 3

Subtract 4 from 27 to find the factorial of the denominator.
${ }_{27} P_{4} = \frac{27!}{23!}$

STEP 4

Expand the factorials in the numerator and denominator to cancel out the common terms.
${ }_{27} P_{4} = \frac{27 \times 26 \times 25 \times 24 \times 23!}{23!}$

STEP 5

Cancel out the common terms in the numerator and the denominator.
${ }_{27} P_{4} = 27 \times 26 \times 25 \times 24$

STEP 6

Calculate the product of the remaining terms to find the exact value of the expression.
${ }_{27} P_{4} = 27 \times 26 \times 25 \times 24$
${ }_{27} P_{4} = 27 \times 26 \times (25 \times 24)$
${ }_{27} P_{4} = 27 \times 26 \times 600$
${ }_{27} P_{4} = 27 \times 15600$
${ }_{27} P_{4} = 421200$
The exact value of the expression ${ }_{27} P_{4}$ is 421,200.

Was this helpful?

Get Studdy

Scan QR code with your device to get Studdy on iOS or Android

QR code

Studdy solves anything!

Download the app

Start learning now

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

Parents Influencer program Contact Policy Terms