Question

A thief is faced with a combination lock with five wheels. Each wheel has the
digits 0 to 9. The correct sequence of 5 digits needed to open the lock has no
repeated digits. What is the probability that the thief will guess the correct
sequence on the first try?

Answer 1

If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.

10^5 = ?

Answer 2

since no digits are to be repeated, the number of possible valid combinations is just the number of permutations of 10 things, taken 5 at a time: 10!/5!

However, unless the burglar knows that, he still has only one chance in 10^5 of getting it right, as PsyDAG showed above.