Please help combo question

Question

A small combination lock on a suitcase has 4 wheels, each labeled with the 10 digits from 0 to 9. If an opening combination is a particular sequence of 4 digits with no repeats what is the probability of a person guessing the right combination?

Answer 1

Since order matters in this problem (i.e. 5678 and 8765 are distinct codes), this is a permutation with no replacement. The formula for a permutation with no replacement is n!/(n-r)!, where n the number of available choices, and r is the number of choices you need to make.

In this problem, n is 10, since there are 10 possible numbers to choose from. R is 4, since there are 4 choices we need to make. Thus, 10!/(10-4)! = 3,628,800/720 = 5,040 possible permutations.