The total number of possible outcomes is 6^4=1296. Of these there are 6*5*4=120 with three dice showing different numbers and one die being anything from 1 to 6, which could, of course, include a fourth different number. We want exactly three. The three dice with different numbers can be 123, 124, 134 or 234, where 1 to 4 identifies the dice, not the numbers on them. So there are 4*120=480 such arrangements. From these we have to eliminate the ones that would give us four different numbers. Half the 480 would include the numbers already rolled and half wouldn't match any of them, because we have already used up half the numbers between 1 and 6. So we're left with 240. (Incidentally, 6*5*4*3=360 is the number of all dice showing different numbers and 240+120=360.) So, 240 out of 1296 is the overall probability of rolling exactly three dice with different numbers, that is 240/1296=5/27=18.52%.