Question

A combination lock has numbers 0-49 on it. How many different 3-digit lock combinations are possible if no digit can be repeated? (HINT: How many numbers are there, including 0 and 49?

Answer 1

To solve for this problem, we have to understand PERMUTATION. It is different from combination since in Permutation , the order of the numbers matter and repetition is not allowed. The formula for permutation is:

`P(n,r)=(n!)/((n-r)!)`

In this problem the value of n is 50 since there are 50 numbers from 0 to 49 and the value of r is 3 since it requires 3-digit combinations. Thus,

`P(50,3)=(50!)/((50-3)!)=(50!)/(47!)=117,600`

Answer: There are 117