Simplify (frac{^{n}P_{3}}{^{n}C_{2}} + ^{n}P_{0})
-
A.
n – 5 -
B.
n – 3 -
C.
2n – 1 -
D.
2n – 3
Correct Answer: Option D
Explanation
(frac{^{n}P_{3}}{^{n}C_{2}} + ^{n}P_{0})
(frac{^{n}P_{3}}{^{n}C_{2}} = frac{n!}{(n – 3)!} ÷ frac{n!}{(n – 2)! 2!})
(frac{n!}{(n – 3)!} times frac{(n – 2)(n – 3)! 2!}{n!} = 2n – 4)
(^{n}P_{0} = frac{n!}{(n – 0)!} = 1)
(frac{^{n}P_{3}}{^{n}C_{2}} + ^{n}P_{0} = 2n – 4 + 1 = 2n – 3)