3 distinct digits are randomly selected from the set of nine digits [1-9]. What is the probability that 9 is selected.
I thought that the probability should be (1/9) + (1/8) + (1/7) since you have to chose 3 DISTINCT numbers from the set and therefore the first time the probability of selecting 9 is (1/9), the second time the probability of selecting 9 is 1/8 since this time you only have to chose a set of 8 digits and similarly the third time it should be (1/7).
But according to my teacher the probability should be (1/9)*3 = 1/3 OR (1/9) + (1/9) + (1/9) = (1/3).
I cannot understand why it should be (1/3) Could someone please tell me the right way to do this.