Question

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 ?

• A. $\frac{2}{275}$
• B. $\frac{1}{501}$
• C. $\frac{1}{504}$
• D. $None$

Answer 1

The correct option is C $\frac{1}{504}$

Let $A_i,i=1,2,3$ be the event that the digit on ith wheel occupies the correct position. Then,

Required probability = $P(A_1\cap A_2\cap A_3)$

$=P\left(A_1\right)P\left(A_2/A_1\right)P(A_3/A_1\cap A_2)$

$=\frac{1}{9}\times \frac{1}{8}\times \frac{1}{7}=\frac{1}{504}$