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The number lock of a suitcase has 4 wheels, each labelled with ten digits, i.e. from 0 to 9. The lock opens with a sequence of four digits with no repeats. What is the probability of a person getting the sequence to open the suitcase?
  • a)
    1/5040
  • b)
    2/5040
  • c)
    4/5040
  • d)
    4!/5040
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
The number lock of a suitcase has 4 wheels, each labelled with ten di...
There are 10C4 4! = 5040 sequences of 4 distinct digits, out of which there is only one sequence in which the lock opens.
Required probability = 1/5040
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Community Answer
The number lock of a suitcase has 4 wheels, each labelled with ten di...
Understanding the Lock Mechanism
The suitcase lock consists of 4 wheels, each displaying the digits from 0 to 9. To open the lock, a unique sequence of four digits must be entered, without any repetitions.
Calculating Total Possible Combinations
- Each wheel can display any of the 10 digits (0-9).
- Since digits cannot repeat in the sequence, the selection process is as follows:
- For the 1st digit, there are 10 options (0-9).
- For the 2nd digit, there are 9 remaining options (since one digit has already been used).
- For the 3rd digit, there are 8 options left.
- For the 4th digit, there are 7 options remaining.
Total Combinations Formula
- The total number of unique sequences (combinations) can be calculated as:
- Total combinations = 10 * 9 * 8 * 7 = 5040
Calculating Probability of Correct Sequence
- There is only 1 specific sequence that opens the lock.
- Therefore, the probability of guessing the correct sequence is:
- Probability = (Number of favorable outcomes) / (Total outcomes)
- Probability = 1 / 5040
Conclusion
The correct answer is option 'A' (1/5040), indicating the low probability of correctly guessing the lock combination on the first attempt. This demonstrates the effectiveness of the lock's design in ensuring security through the use of a limited number of unique sequences.
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