The problem states that there is a combination lock with 5 wheels, each labeled with the 10 digits from 0 to 9, and the opening combination is a sequence of 5 digits with no repeats. We need to find the probability of guessing the right combination.

Solution:

• The total number of possible 5-digit combinations without repeats can be calculated using permutations because the order of the digits matters and there are no repetitions.

  The first digit can be any of the 10 digits. Once the first digit is chosen, there are 9 choices left for the second digit, 8 for the third, 7 for the fourth, and 6 for the fifth digit.

  So, the total number of possible combinations is: $10 \times 9 \times 8 \times 7 \times 6 = 30240$

• Since there is only one correct combination, the probability of guessing the right one is: $\text{Probability} = \frac{1}{30240}$

Thus, the probability of guessing the right combination is $\frac{1}{30240}$.

Would you like more details or have any questions?

Related Questions:

1. What is the total number of combinations if repetitions were allowed?
2. How does the probability change if the lock had 6 wheels instead of 5?
3. What if only 4 digits were used instead of 5? How would that affect the probability?
4. How would the probability change if there were 12 digits (from 0 to 11) instead of 10?
5. What is the probability of guessing the correct combination on the second try?

Tip:

When calculating probabilities for permutations, remember that the order of the items affects the total number of outcomes.