Question

A number lock consists of 3 rings each marked with 10 different numbers. In how many cases the lock cannot be opened?

• A. 3
• B. 10
• C. 30
• D. 999

Answer 1

The Correct Option is D

The problem involves a number lock with 3 rings, where each ring is numbered from 0 to 9. Therefore, each ring has 10 possible positions it can be set to.

To find the total number of combinations for the lock, we consider all the possible positions each ring can take independently of the others. Since there are 3 rings, the total number of possible combinations is calculated using the fundamental principle of counting, which is the product of the possibilities for each independent event.

Thus, the total number of combinations for the lock is:

10 × 10 × 10 = 1000

Since the question asks for the number of situations in which the lock cannot be opened, we should account for the case where none of the combinations work.

Assuming the lock can be opened with exactly one specific combination, this means that out of the 1000 possible combinations, there is exactly 1 combination that opens the lock, leaving:

1000 - 1 = 999

Thus, the number of cases where the lock cannot be opened is 999.