Permutation and Combination  Quant/Math  CAT 2016
Question 4 the day:
September 02, 2003
The question for the day is from the topic Permutation and Combination.
Question:
 When four fair dice are rolled simultaneously, in how many outcomes will at least one of the dice show 3?
(1) 155
(2) 620
(3) 671
(4) 625
Correct Answer  (3)
Solution:
When 4 dice are rolled simultaneously, there will be a total of 6^{4} = 1296 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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