Answer to Question #299240 in Discrete Mathematics for Philly

Question

A home security system has a pad with 9 digit (1 to 9 ). Find the number of possible 5-digit pass code if digit can be repeated or if digit cannot be repeated

Answer 1

If the digits can be repeated the number of possible 5-digit codes is 9*9*9*9*9 = 9⁵ = 59049)

(The first place may occupy any of the nine digits, and so for second, third, fourth, and fifth places)

If the digits can't be repeated the number of combinations is 9*8*7*6*5 = 15120

(The first place may occupy any of the nine digits, the second only one of eight remainings, and so on)