Permutation & Combination Answers

Permutation and Combination - Quant/Math - CAT 2007

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Question 4 the day: September 16, 2002

The question for the day is from the topic Permutation and Combination.

Question:

Four dice are rolled simultaneously. What is the number of possible outcomes in which at least one of the die shows 6?

(1) 6! / 4!
(2) 625
(3) 671
(4) 1296

Correct Answer - (3)

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Solution:

When 4 dice are rolled simultaneously, there are 6⁴ = 1296 outcomes. The converse of what is asked in the question is that none of the dice show '6'. That is all four dice show any of the other 5 numbers. That is possible in 5⁴ = 625 outcomes.

Therefore, in 1296 - 625 = 671 outcomes at least one of the dice will show 6.