Probability question

Im really stuck on this question

Three dice are thrown. Find the probability of obtaining different scores on all the dice.

The answer is 0.5556 but i cant get anywhere near this..

For them all to take different values, the first die has 6 options. The second die has 5 options, and the third die has 4 leftover options.

The total number of ways in which we have a resulting roll where all three dice have different numbers is precisely 6 x 5 x 4 ... or if you will, (6 P 3) which denotes the number of ways we can pick 3 numbers out of 6 where order matters.

Now you just need to obtain the probability of rolling a particular combination.

Then multiply this by (6 P 3) as this imposes that your probability concerns only the cases where we roll three distinct numbers.

For them all to take different values, the first die has 6 options. The second die has 5 options, and the third die has 4 leftover options.

The total number of ways in which we have a resulting roll where all three dice have different numbers is precisely 6 x 5 x 4 ... or if you will, (6 P 3) which denotes the number of ways we can pick 3 numbers out of 6 where order matters.

Now you just need to obtain the probability of rolling a particular combination.

Then multiply this by (6 P 3) as this imposes that your probability concerns only the cases where we roll three distinct numbers.

Sorry im still confused. I get that theres 120 ways of rolling the 3 dice so that they show different scores.

But what do u mean by "Now you just need to obtain the probability of rolling a particular combination."

Would that not be (6/6)x(5/6)x(4/6)?

Consider an arbitrary combination. Eg. (1,2,5)

What is the probability that this combination is obtained?

This is what I mean.