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)
0 7,776
1
7,776
100,000
1
100,000

Answer 1

To determine the probability of guessing the correct combination for a 5-digit lock using numbers from 1 to 6, we first need to calculate the total number of possible combinations.

Each digit in the combination can be one of 6 numbers (1 through 6), and since there are 5 digits, the total number of combinations can be calculated using the formula:

\[
\text{Total combinations} = 6^5
\]

Calculating that:

\[
6^5 = 6 \times 6 \times 6 \times 6 \times 6 = 7776
\]

Therefore, there are 7776 possible combinations.

When you are guessing, there is only 1 correct combination out of the 7776 possible combinations.

The probability of guessing the correct combination is therefore:

\[
\text{Probability} = \frac{1 \text{ (successful guess)}}{7776 \text{ (total combinations)}} = \frac{1}{7776}
\]

Therefore, the correct answer is:

\[
\text{Probability} = \frac{1}{7776}
\]