Given that (^{n}P_{r} = 90) and (^{n}C_{r} = 15), find the value of r.
-
A.
2 -
B.
3 -
C.
5 -
D.
6
Correct Answer: Option 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)