probability - 4 dice are rolled, what is the probability that one die will show a number appearing on one of the other dice?

Vivekanand Vellanki (last edited 4 years ago) (Expert, Founder @Qalaxia)

Let P be the probability that all 4 dice roll different numbers.

The probability that one die will show a number appearing on one of the other dice would be 1 - P. I have to assume that this means "at least one die" as the question is not clear about this.

P=\frac{\left(6\cdot5\cdot4\cdot3\right)}{6\cdot6\cdot6\cdot6}. The first die can roll any number - hence, it has 6 choices. The 2nd die cannot roll the number rolled by the first die - hence, it has 5 choices and so on.

The fact that all the dice are rolled simultaneously does not change P.