# Thread: having trouble counting the elements in my event,probability space (its basic)

1. ## having trouble counting the elements in my event,probability space (its basic)

i was given this problem on one of my courses

four numbers are chosen independently at random from the numbers 1...10 (allowing for repetitions) what is the probability that they are all different,

so i count the number of elements in my probability space 10^4
and the number of elements in my event space 10 choose 4
and divide the second by the first,
i get the wrong answer if i do this though,
if someone could tell me where i have gone wrong that would be great thanks very much

2. Originally Posted by hmmmm
i was given this problem on one of my courses

four numbers are chosen independently at random from the numbers 1...10 (allowing for repetitions) what is the probability that they are all different,

so i count the number of elements in my probability space 10^4
and the number of elements in my event space 10 choose 4
and divide the second by the first,
i get the wrong answer if i do this though,
if someone could tell me where i have gone wrong that would be great thanks very much
1234 differs from 4321, so you desire numerator 10P4 = 10C4 * 4!.

3. yeah thanks very much