A combination lock on a suitcase has 3 wheels, each labelled 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 ?

Explanation

Let` {A}_{{i}}, {i}=1,2,3` be the event that the digit on ith wheel occupies the correct position.


Required probability `=P(A_{1} cap A_{2} cap A_{3})`


`=P(A_{1}) P(A_{2}) / (A_{1}) P(A_{3} / A_{1} cap A_{2})`


`=frac{1}{9} \times\ frac{1}{8}\ times \frac{1}{7}`


`=frac{1}{504}`