Question

7.4
score: 3/17 answered: 3/17
question 4
evaluate.
$p(8,4) = $
question help: ebook written example

Explanation:

Step1: Recall permutation formula

The permutation formula is \( P(n, r)=\frac{n!}{(n - r)!} \), where \( n = 8 \) and \( r = 4 \).

Step2: Substitute values into formula

Substitute \( n = 8 \) and \( r = 4 \) into the formula: \( P(8, 4)=\frac{8!}{(8 - 4)!}=\frac{8!}{4!} \).

Step3: Expand factorials

We know that \( n!=n\times(n - 1)\times\cdots\times1 \), so \( 8! = 8\times7\times6\times5\times4! \) and \( 4! = 4\times3\times2\times1 \). Then \( \frac{8!}{4!}=\frac{8\times7\times6\times5\times4!}{4!} \).

Step4: Simplify the expression

Cancel out \( 4! \) in the numerator and denominator: \( 8\times7\times6\times5 \).

Step5: Calculate the product

\( 8\times7 = 56 \), \( 56\times6 = 336 \), \( 336\times5 = 1680 \).

Answer:

\( 1680 \)