# Difficult Permutation-Combination Solved QuestionAptitude Discussion

 Q. When four fair dice are rolled simultaneously, in how many outcomes will at least one of the dice show 3?
 ✖ A. 155 ✖ B. 620 ✔ C. 671 ✖ D. 625

Solution:
Option(C) is correct

When 4 dice are rolled simultaneously, there will be a total of $6^4 = 1,296$ outcomes.

The number of outcomes in which none of the 4 dice show 3 will be $5^4= 625$ outcomes.

Therefore, the number of outcomes in which at least one die will show 3:

$= 1296 – 625$

$= 671$