Phil rolls 6 fair 6-sided dice. What is the probability that at least two dice show the same number?

Are the dice all the same or all different, colours or sizes I mean?

It is complicated either way but it does make a difference.

It would be 1 - the prob of 2 not being the same.

= 1- the prob that they are all different.

If the dice are all different then there are 6! way that they can be all different.

If the dice are all different then there are 6^6 variations on what can be thrown.

So prob that they are all different = \(\frac{6!}{6^6}\)

and the probability that they ar not all different = \(1-\frac{6!}{6^6}\)

1-6!/(6^6) = 0.9845679012345679 

so the prob that at least 2 die show the same number is about 98.5%

Why would a difference in the dice (assuming it does not affect the fairness) make the probability outcomes different?