Question

perform the indicated calculation.

\frac{5 p_{3}}{11 p_{4}}

\frac{5 p_{3}}{11 p_{4}}=\square (round to four decimal places as needed.)

Explanation:

Step1: Recall permutation formula

The permutation formula is \(_{n}P_{r}=\frac{n!}{(n - r)!}\).
For \(_{5}P_{3}\), \(n = 5\), \(r=3\), so \(_{5}P_{3}=\frac{5!}{(5 - 3)!}=\frac{5!}{2!}=\frac{5\times4\times3\times2!}{2!}=5\times4\times3 = 60\).
For \(_{11}P_{4}\), \(n = 11\), \(r = 4\), so \(_{11}P_{4}=\frac{11!}{(11-4)!}=\frac{11!}{7!}=\frac{11\times10\times9\times8\times7!}{7!}=11\times10\times9\times8=7920\).

Step2: Calculate the ratio

\(\frac{_{5}P_{3}}{_{11}P_{4}}=\frac{60}{7920}\).
Simplify \(\frac{60}{7920}=\frac{1}{132}\approx0.0076\).

Answer:

\(0.0076\)