Question:

A number lock on a suitcase has 3 wheels each labelled with 10 digits from 0 to 9. If opening of the lock is a particular sequence of three digits with no repeats, how many such sequences will be possible?

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Use the permutation formula \( P(n, r) = \frac{n!}{(n-r)!} \) when order matters and there are no repetitions.
Updated On: Mar 7, 2025
  • 720
  • 760
  • 680
  • 780
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The Correct Option is A

Solution and Explanation

The first wheel has 10 choices, the second has 9 choices (no repeats), and the third has 8 choices: \[ 10 \times 9 \times 8 = 720 \] Thus, the number of such sequences possible is 720.
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