Question

If$n ⥂ P_{4}:^{n}P_{5} = 1:2$, then $n =$

• A. 4
• B. 5
• C. 6
• D. 7

Answer 1

Answer: (C)

6

Answer 2

$\frac{nP_{4}}{nP_{5}} = \frac{1}{2}$ ⇒ $\frac{n!}{(n - 4)!} \times \frac{(n - 5)!}{n!} = \frac{1}{2}$ ⇒ $n - 4 = 2$ ⇒ $n = 6$.