A numerical lock can be opened using any possible combination of these five digits 0, 1, 0, 3 and 2 (example 20031). John used all possible incorrect combinations on the 5-digit lock before finally opening the lock at the next attempt. How many total attempts did he make? The digits available are 0-5 in lock
Question
A numerical lock can be opened using any possible combination of these five digits 0, 1, 0, 3 and 2 (example 20031). John used all possible incorrect combinations on the 5-digit lock before finally opening the lock at the next attempt. How many total attempts did he make? The digits available are 0-5 in lock
Solution
The lock can be opened with any combination of the five digits 0, 1, 0, 3, and 2. This means that the digits can be repeated in the combination.
Step 1: Determine the total number of possible combinations.
Since there are 5 slots to fill and each slot can be filled by any of the 5 digits, the total number of possible combinations is 5^5 = 3125.
Step 2: Subtract the correct combination.
John used all possible incorrect combinations before finally opening the lock. This means he tried 3125 - 1 = 3124 incorrect combinations.
Step 3: Add the final correct attempt.
John finally opened the lock at the next attempt, so we add this final attempt to the total.
So, John made 3124 + 1 = 3125 total attempts.
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