Simplify (frac{^{n}P_{5}}{^{n}C_{5}}).
-
A.
80 -
B.
90 -
C.
110 -
D.
120
Correct Answer: Option D
Explanation
(frac{^{n}P_{5}}{^{n}C_{5}} = frac{n!}{(n-5)!} ÷ frac{n!}{(n-5)!5!})
= (frac{n!}{(n-5)!} times frac{(n-5)!5!}{n!} = 5! = 120)
Simplify (frac{^{n}P_{5}}{^{n}C_{5}}).
(frac{^{n}P_{5}}{^{n}C_{5}} = frac{n!}{(n-5)!} ÷ frac{n!}{(n-5)!5!})
= (frac{n!}{(n-5)!} times frac{(n-5)!5!}{n!} = 5! = 120)