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?

• A. 720
• B. 760
• C. 680
• D. 780

Hint:

Use the permutation formula \( P(n, r) = \frac{n!}{(n-r)!} \) when order matters and there are no repetitions.

Answer 1

The Correct Option is A

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.