To Find: Value of n
Given: (n+1)! = 12× [(n-1)!]
Formula Used: n! = (n) × (n-1) × (n-2) × (n-3) ………. 3 × 2 × 1
Now, (n+1)! = 12× [(n-1)!]
⇒ (n+1) × (n) × [(n-1)!] = 12 × [(n-1)!]
⇒ (n+1) × (n) = 12
⇒ n2+n = 12
⇒ n2+n-12 = 0
⇒ (n-3) (n+4) = 0
⇒ n = 3 or, n = -4
But, n=-4 is not possible because in case of factorial (!) n cannot be negative. Hence, n=3 is the correct answer.