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A number lock on a suitcase has 3 wheels each labeled with 10 digits from 0 to 9. If the opening of the lock requires a particular sequence of four digits with no repeats, how many such sequences will be possible?Choices:- 4224 720 560 5040

Question

A number lock on a suitcase has 3 wheels each labeled with 10 digits from 0 to 9. If the opening of the lock requires a particular sequence of four digits with no repeats, how many such sequences will be possible?Choices:- 4224 720 560 5040

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Solution

The problem seems to have a discrepancy. It mentions that the lock has 3 wheels but requires a sequence of 4 digits. Assuming the lock has 4 wheels, here's how you can solve it:

Step 1: For the first wheel, you have 10 choices (0 to 9).

Step 2: For the second wheel, since no digit can be repeated, you have 9 remaining choices.

Step 3: For the third wheel, you have 8 remaining choices.

Step 4: For the fourth wheel, you have 7 remaining choices.

To find the total number of possible sequences, you multiply the number of choices for each wheel together. So, the answer is 1098*7 = 5040.

Therefore, the correct answer is 5040.

This problem has been solved

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