Question

A small combination lock on a suitcase has 3 ​wheels, each labeled with the 10 digits from 0 to 9. If an opening combination is a particular sequence of 3 digits with no​ repeats, what is the probability of a person guessing the right​ combination?

Answer 1

0.14% probability of a person guessing the right​ combination

Explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

The order in which the numbers are selected is important. For example, 1,3,2 is a different combination than 3,1,2. So we use the permutations formula to solve this question.

Permutations formula:

The number of possible permutations of x elements from a set of n elements is given by the following formula:

`P_((n,x)) = (n!)/((n-x)!)`

Desired outcomes:

One right combination, so
`P = 1`

Total outcomes:

10 numbers from a set of 3. So

`P_((10,3)) = (10!)/((10-3)!) = 720`

What is the probability of a person guessing the right​ combination?

`p = (D)/(T) = (1)/(720) = 0.0014`

0.14% probability of a person guessing the right​ combination