Permutation and Combination  Quant/Math  CAT 2016
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)
Solution:
When 4 dice are rolled simultaneously, there are 6^{4} = 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 5^{4} = 625 outcomes.
Therefore, in 1296  625 = 671 outcomes at least one of the dice will show 6.
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