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# What is the probability of getting a sum of 12 when rolling

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Senior Manager
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What is the probability of getting a sum of 12 when rolling [#permalink]  17 Apr 2006, 05:47
31. What is the probability of getting a sum of 12 when rolling 3 dice simultaneously?

a) 10/216
b) 12/216
c) 21/216
d) 23/216
e) 25/216
Manager
Joined: 09 Apr 2006
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Ans E.

We need to detect the # of combinations that add up to 12 with three dices. Here are the details -

a. 6,4,2 = can arrange in 6 ways.
b. 5,5,2 = can arrange in 3 ways.
c. 3,3,6 = can arrange in 3 ways.
d. 6,5,1 = can arrange in 6 ways.
e. 3,4,5 = can arrange in 6 ways.
f. 4,4,4 = can arrange in 1 ways.

So there are 6 + 3 + 3 + 6 + 6 + 1 = 25 ways.

The number of total possibilities is 6*6*6 = 216.

So the probability is 25/216.
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Thanks,
Zooroopa

Senior Manager
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Yeah i think this is what I need to understand

how? 5,5,2 = can arrange in 3 ways.
how? 3,3,6 = can arrange in 3 ways.

GmatAcer!
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gmatacer wrote:
Yeah i think this is what I need to understand

how? 5,5,2 = can arrange in 3 ways.
how? 3,3,6 = can arrange in 3 ways.

GmatAcer!

In general, for permutation of n things, with p things alike (out of n), the permutations are n!/p!. This is because the n! includes p! permutations of those p things, which is not correct.

Therefore, in this case, 5, 5, 2 can be arranged in 3!/2! ways = 3.
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Who says elephants can't dance?

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Joined: 07 Apr 2006
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the arrangements are

552,255,525

got it
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go,get it........

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