To open the suitcase lock, the correct sequence of numbers must be set. Let’s analyze the situation:

Total Possible Combinations

Each wheel of the lock has 10 digits (0 to 9). Since there are 3 wheels, the total number of possible combinations is:

$10 \times 10 \times 10 = 1000$

Successful Combination

There is only 1 specific sequence that opens the lock.

Unsuccessful Attempts

The number of unsuccessful attempts is the total number of combinations minus the one successful attempt:

$1000 - 1 = 999$

Final Answer

• Yes, opening the lock is possible with a specific sequence.
• The number of unsuccessful attempts is 999.

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Do you want further clarification or have any questions? 😊

Related Questions:

1. How does the probability of success change if there are more wheels or fewer digits on each wheel?
2. What is the probability of guessing the correct combination on the first attempt?
3. How many attempts would it take, on average, to open the lock if guesses are random?
4. If the lock had 4 wheels instead of 3, how many unsuccessful attempts would there be?
5. How can combinations be reduced using patterns or constraints (e.g., only even numbers)?

Tip:

When solving problems with permutations or combinations, remember to account for constraints or repetitions carefully to avoid overestimating results!