# A combination lock on a suitcase has 3 wheels, each labeled with nine digits from 1 to 9.

Question:

A combination lock on a suitcase has 3 wheels, each labeled with nine digits from 1 to 9. If an opening combination is a particular sequence of three digits with no repeats, what is the probability of a person guessing the right combination?

Solution:

As repetition is not allowed total no.of cases possible is

$9 \times 8 \times 7$ (because if one of the numbers occupies a wheel, then the other wheel cannot be occupied by this number, i.e. next wheel have 1 less case than the previous wheel and so on)

Therefore, total cases $=504$

Desired output is the correct combination of a single 3 digit number.

Therefore, the total no.of desired outcomes are 1

We know that,

Probability of occurrence of an event

$=\frac{\text { Total no.of Desired outcomes }}{\text { Total no.of outcomes }}$

Therefore, the probability of correct combination

$=\frac{1}{504}$

Conclusion: Probability of guessing right combination is $\frac{1}{504}$