Permutation & Combination Answers

Permutation and Combination - Quant/Math - CAT 2007

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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)

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Solution:


When 4 dice are rolled simultaneously, there will be a total of 6⁴ = 1296 outcomes.

The number of outcomes in which none of the 4 dice show 3 will be 5⁴ = 625 outcomes.

Therefore, the number of outcomes in which at least one die will show 3 = 1296 � 625 = 671