What is the probability that a 10-sided die is rolled 3 times and each time the value was unique (i.e. there are no repeating values from previous rolls)?

Question

I know I can do this with a tree diagram fairly easily, but is there a formula for it that doesn't involve one of those? They're time-consuming.

Answer 1

On the first roll, there are 10 possible outcomes.
For the second roll you want it to be different from the first, so only 9 possible outcomes, with 8 as the third

So the prob(your event) = 10*9/8/1000
= .72

Answer 2

Ah awesome! Any specific reason we're dividing by 1000? Just to get the right decimal?

Answer 3

Multiplication rule:
(10/10)*(9/10)*(8/10)=10*9/8/1000