Question

a certain 5 - digit combination lock can be reset with a new combination. the lock uses numbers from 1 to 6. after a friend accidentally resets it to an unknown combination, what is the probability that you guess the combination that opens the lock?
(1 point)
7,776
1/7,776
100,000
1/100,000

Explanation:

Step1: Calculate total number of combinations

Each digit has 6 choices (1 - 6). For a 5 - digit combination, by the multiplication principle, the total number of combinations is \(6\times6\times6\times6\times6=6^{5}\).

$$6^{5}=7776$$

Step2: Calculate probability

Probability \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\). There is 1 favorable outcome (the correct combination). So \(P = \frac{1}{7776}\)

Answer:

\(\frac{1}{7776}\) (the second option)