Question

The numbers 1 through 9 are written in separate slips of paper, and the slips are placed into a box. Then, 4 of these slips are drawn at random.

What is the probability that the drawn slips are "1", "2", "3", and "4", in that order?

Answer 1

The probability of drawing the slips '1', '2', '3', and '4' in that order is 1/126 or approximately 0.0079.

Step-by-step explanation:

The probability that the drawn slips are '1', '2', '3', and '4', in that order, can be calculated by considering the number of favorable outcomes and the total number of possible outcomes.

There are 9 slips in the box, so the total number of possible outcomes is 9 choose 4, which is denoted as C(9,4) or 9!/(4!(9-4)!), which simplifies to 126.

Since we want the slips to be drawn in a specific order, the number of favorable outcomes is 1, because there is only 1 way to arrange the slips in the order '1', '2', '3', and '4'.

Therefore, the probability is 1/126, which simplifies to approximately 0.0079 or 0.79%.

Answer 2

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

`(1)/(3024)= 0.00033`


We could have solved this problem also as :

P(drawing 1, 2, 3, 4 in order)=
`(1)/(9) * (1)/(8) * (1)/(7) * (1)/(6) = (1)/(3024)`

Answer:
`(1)/(3024)= 0.00033`