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Fair sided die - Probability

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by neelgandham » Fri Nov 04, 2011 8:35 am
A fair sided die labeled 1 to 6 is tossed three times. What is the probability the sum of the 3 throws is 16?

A)1/6
B)7/216
C)1/36
D)9/216
E)11/216
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by user123321 » Fri Nov 04, 2011 8:49 am
possibilities can be
5,5,6 =>3!/2! = 3 ways
6,6,4 =>3!/2! = 3 ways

so probability is (3+3)/6^3 = 1/36

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by gmatblood » Fri Nov 04, 2011 8:56 am
IMO:C
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by Anurag@Gurome » Fri Nov 04, 2011 11:02 pm
neelgandham wrote:A fair sided die labeled 1 to 6 is tossed three times. What is the probability the sum of the 3 throws is 16?

A)1/6
B)7/216
C)1/36
D)9/216
E)11/216
Since the die is tossed 3 times, total number of possible outcomes = 6^3 = 216
Now possible combinations is 3 throws when the sum can be 16 are: (4, 6, 6), (6, 4, 6), (6, 6, 4), (5, 5, 6), (6, 5, 5), (5, 6, 5).
So, number of ways in which a sum of 16 can be obtained = 6
So, required probability = 6/216 = [spoiler]1/36[/spoiler]

The correct answer is C.
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