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miv72 [106K]
3 years ago
8

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?
Mathematics
1 answer:
Artyom0805 [142]3 years ago
5 0

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

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