If 5* ⁿP₃ = 4* ⁽ⁿ⁺¹⁾P₃, find n?

Explanation:-

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 = [n! /(n -r)!].