Let's think of the problem as follows.
Write all the 4-digit numbers that can be formed using the digits from 1 to 9, without repetition, in pieces of paper, and put them in a bag. What is the probability of picking the 4-digit number 1234, among these numbers.
The connection of the 2 problems is as follows:
The 4-digit number, for example 5489, represents drawing first 5, then 4, then 8, then 9 , in the original question.
we did not allow repetition, because for example the number 8918 would represent drawing 8, then 9, then 1 then 8 (again!!), which is not possible, so we lose the connection between the problems.
So there are in total 9*8*7*6= 3024 4-digit numbers, with non-repeating digits.
One of these numbers is 1234 (representing drawing 1, then 2, then 3, then 4)
among these 3024 numbers, the probability of picking 1234 is
[tex] \frac{1}{3024}= 0.00033[/tex]
We could have solved this problem also as :
P(drawing 1, 2, 3, 4 in order)= [tex] \frac{1}{9} * \frac{1}{8} * \frac{1}{7} * \frac{1}{6} = \frac{1}{3024} [/tex]
Answer:[tex] \frac{1}{3024}= 0.00033[/tex]
