If 5 × ^ n P_3 = 4 × ^ ( n + 1 ) P_3, find n?

Answer: Option D

ⁿP₃ = n × (n–1) × (n–2)
⁽ⁿ⁺¹⁾P₃ = (n+1) × n × (n–1)
Now,
5 × n × (n–1) × (n–2) = 4 × (n+1) × n × (n–1)
Or, 5(n−2) = 4(n+1)
Or, 5n − 10 = 4n + 4
Or, 5n − 4n = 4 + 10
Hence, n = 14

Note: ⁿP_r = $$\frac{\text{n}!}{\left(\text{n}-\text{r}\right)!}$$