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

Answer:

0.14% probability of a person guessing the right​ combination

Step-by-step 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:

$P_{(n,x)} = \frac{n!}{(n-x)!}$

Desired outcomes:

One right combination, so $P = 1$

Total outcomes:

10 numbers from a set of 3. So

$P_{(10,3)} = \frac{10!}{(10-3)!} = 720$

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

$p = \frac{D}{T} = \frac{1}{720} = 0.0014$

0.14% probability of a person guessing the right​ combination