5. How many different

codes can a combination

lock have if there are three

numbers on the lock and

each number can be from

0-9?

Correct answer: Vr = 10³ = 1,000 or V = 720

Step-by-step explanation:

Given:

Input set of numbers S = {0, 1, 2, ... 9} ⇒ x = 10

A string that changes n = 3

I guess the numbers can be repeated as 1,1,1 or 2,3,2 ...

then these are variations with repetition and the formula is:

Vr (x n) = xⁿ

Vr (10 3) = 10³ = 1,000

if the numbers cannot be repeated then these are variations without repeating and the formula is:

V = (x n) = x (x - 1) (x - 2) ... (x - n + 1)

(10 - 3 + 1) = 8

V = (10 3) = 10 ·9 · 8 = 720

God is with you!

Answer: A three digit combination with a selection of 1 - 9 (Nine numbers) would have 729 combinations,