Question

The numbers 1 through 10 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

Since you want those numbers to appear in that precise order, you only change is to extract 1 with the first draw, 2 with the second, and so on.

You have 10 slips at the beginning, so the probability of having 1 at the first draw is

`(1)/(10)`

Now you have 9 slips left, so the probability of picking 2 with the second draw is

`(1)/(9)`

Similarly, the remaining probabilities are
`(1)/(8)` and
`(1)/(7)`

You want these events to happen one after the other, and they are independent. So, the overall probability is the product of the single probabilities:

`P = (1)/(10)\cdot(1)/(9)\cdot(1)/(8)\cdot(1)/(7) = (1)/(10\cdot9\cdot8\cdot7) = (1)/(5040)`