Question

perform the indicated calculation.

\\\frac{_{5}p_{2}}{_{12}p_{4}}\\

\\\frac{_{5}p_{2}}{_{12}p_{4}} = \text{ } (\text{round to four decimal places as needed.})\\

Explanation:

Define permutation formula

Using the Combinatorics knowledge point

$$ _n P_r = \frac{n!}{(n-r)!} $$

Calculate the numerator

Using the Combinatorics knowledge point

$$ _5 P_2 = \frac{5!}{(5-2)!} = \frac{5 \times 4 \times 3!}{3!} = 5 \times 4 = 20 $$

Calculate the denominator

Using the Combinatorics knowledge point

$$ _{12} P_4 = \frac{12!}{(12-4)!} = \frac{12 \times 11 \times 10 \times 9 \times 8!}{8!} = 12 \times 11 \times 10 \times 9 = 11880 $$

Compute the final ratio

Using the Combinatorics knowledge point

$$ \frac{_5 P_2}{_{12} P_4} = \frac{20}{11880} = \frac{2}{1188} = \frac{1}{594} \approx 0.0016835 $$

Round to four decimal places

Using the Combinatorics knowledge point

$$ 0.0016835 \approx 0.0017 $$

Answer:

Perform the indicated calculation.

$$\frac{_5P_2}{_{12}P_4} =$$

<blank>\(0.0017\)</blank> (Round to four decimal places as needed.)