Factorials - If (n + 2)! = 2550 (n!), find n?

Question:

If (n + 2)! = 2550 (n!), find n?


Solution:

(n + 2)! = 2550 (n!)

(n + 2)! / (n!) = 2550

∴ [(n + 2) (n + 1) n!] / n! = 2550

∴ [(n + 2) (n + 1) ̶n̶!̶] / ̶n̶!̶ = 2550

∴ [(n + 2) (n + 1)] / = 2550

∴ [(n + 2) (n + 1)] / = 51 x 50

∴ By comparison

n + 2 = 51

∴ n = 49


Answer:

If (n + 2)! = 2550 (n!), n = 49.


Video Solution:



If (n + 2)! = 2550 (n!), find n? A solved exmaple on Factorials in Permutations and Combinations