Permutation and Combination - Quant/Math -
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Question 4 the day: September 16, 2002
The question for the day is from the topic of Permutation and Combination.

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

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.