Given that \(^{n}P_{r} = 90\) and \(^{n}C_{r} = 15\), find the value of r.
- 2
-
3
- 5
- 6
The correct answer is: B
Explanation
\(\frac{^{n}P_{r}}{^{n}C_{r}} = \frac{\frac{n!}{(n - r)!}}{\frac{n!}{(n - r)! r!}} = \frac{90}{15} = 6\)
\(\frac{n!}{(n - r)!} \times \frac{(n - r)! r!}{n!} = r! = 6\)
\(r = 3\)