Question

The number lock of a suitcase has 4 wheels, each labelled with ten digits i.e., from 0 to 9. The lock opens with a sequence of four digits with no repeats. What is the probability of a
person getting the right sequence to open the suitcase?

Answer 1

There are total 10 digits from 0 to 9. Since the digits cannot be repeated.
So the first place may filled in 10 ways, second place in 9 ways, third place in 8 ways and fourth place in 7 ways.
$\therefore$ Number of possible outcomes
$=10\times 9\times 8\times 7=5040$
The lock of suitcase can be opened in 1 way only
$\therefore$ Number of favourable cases = 1
Thus required probability $=\frac{1}{5040}$