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 right sequence to open the suitcase?
The probability of getting the right sequence to open the suitcase is 1/5040.
Explanation
This question tests the understanding of permutations and probability. Since there are no repeats allowed, we use the permutation formula. The total number of possible sequences is calculated using the multiplication principle, and since only one specific sequence opens the lock, the probability is 1 divided by the total number of sequences.
Solution Steps
Step 1: Identify the total number of digits available. Each wheel has 10 digits (0 to 9).
Step 2: Calculate the total number of possible sequences with no repeats. For the first digit, there are 10 choices. For the second digit, there are 9 choices (since repetition is not allowed). For the third digit, there are 8 choices. For the fourth digit, there are 7 choices. Total number of sequences = × = 5040.
Step 3: Determine the number of favorable outcomes. There is only 1 correct sequence that opens the lock.
Step 4: Calculate the probability. Probability = Number of favorable outcomes / Total number of possible outcomes = 1/5040.