Question

You pick 4 digits (0-9) at random without replacement, and write them in the order picked. what is the probability that you have written the first 4 digits of your phone number? assume there are no repeats of digits in your phone number.

Answer 1

The number of ways of choosing 4 digits from 10 digits without replacement ( order is important) is $P(10,4)=\frac{10!}{(10-4)!} =\frac{10!}{(6)!} =7*8*9*10=5040$. This is the number of all possible permutations of choosing 4 from 10. The first 4 numbers of your phone number is a unique 4 digit number(4 different digits). The required probability is

$\frac{1}{5040}$