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