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?

7,776
1/7,776
100,000
1/100,000

Answer 1

To find the total number of possible 5-digit combinations for the lock, we consider that each digit can be any number from 1 to 6.

For each of the 5 positions in the combination, there are 6 possible choices (since the numbers can be 1, 2, 3, 4, 5, or 6). Therefore, the total number of combinations can be calculated as:

\[
6^5
\]

Calculating \(6^5\):

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

So, there are a total of 7,776 distinct combinations.

Since you are trying to guess the correct combination from these 7,776 possibilities, the probability of guessing the correct combination is given by the formula:

\[
\text{Probability} = \frac{\text{Number of successful outcomes}}{\text{Total number of outcomes}} = \frac{1}{7776}
\]

Thus, the probability that you guess the combination that opens the lock is:

\[
\frac{1}{7776}
\]

The correct answer is:

**1/7,776**