Discussion
If \(9_{p5} = (504)({}^{6}P_{r})\) , then the value of \(r\) is equal to
Answer: B
\(r = 2\).
Reading the left side as \({}^{9}P_{5}\):
\[ \begin{aligned} {}^{9}P_{5} &= 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 = 15120 \\ {}^{6}P_{r} &= \frac{15120}{504} = 30 \end{aligned} \]
Since \({}^{6}P_{2} = 6 \times 5 = 30\), \(r = 2\). The other values give \({}^{6}P_{1} = 6\), \({}^{6}P_{3} = 120\), \({}^{6}P_{4} = 360\) and \({}^{6}P_{5} = 720\).
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