With four dice is it easier to roll 4 of a kind or 4 different ones?

Question

I have an argue with my friend. I say its harder to roll four of a kind, but i cant explain my logic. Please help me figure this out.

Answer 1

There are 6 ways to roll 4 of a kind each with probability (1/6)⁴, i.e. probability (1/6)³.

 

There are ₆P₄ ways of rolling 4 different faces in 4 rolls each of these ways has probability (1/6)⁴, i.e. probability

360 * (1/6)⁴ = 60 * (1/6)³.

 

Therefore, you are correct.