Permutation-Combination
Aptitude

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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

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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:

$= 1296 – 625$

$= 671$


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