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# What is the probability that you will get a sum of 8 when

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Manager
Joined: 05 Nov 2012
Posts: 170
What is the probability that you will get a sum of 8 when [#permalink]

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18 Nov 2012, 16:07
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What is the probability that you will get a sum of 8 when you throw three dice simultaneously?

Similarly, What is the probability that you will get a sum of 22 when you throw four dice simultaneously?
Manager
Joined: 05 Nov 2012
Posts: 170
Re: What is the probability that you will get a sum of 8 when [#permalink]

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18 Nov 2012, 16:11
here is my approach for first case......
total number of possible cases is 6*6*6 (3 die, 6 cases on each)
sum to be 8
1,1,6
1,2,5
1,3,4
possible combinations.... but since each case don't need to be in orer... each case can happen as 3! ways on die .....so prob is 3!*3/6*6*6=3/36=1/12
is this correct?
problem is in the second case.... when number of die increase I am going to kill time... what should be the approach? Thanks
Math Expert
Joined: 02 Sep 2009
Posts: 39744
Re: What is the probability that you will get a sum of 8 when [#permalink]

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19 Nov 2012, 03:17
Amateur wrote:
What is the probability that you will get a sum of 8 when you throw three dice simultaneously?

Similarly, What is the probability that you will get a sum of 22 when you throw four dice simultaneously?

What is the probability that you will get a sum of 8 when you throw three dice simultaneously?

This sum of 8 can occur in the following cases:
1-1-6 --> 3!/2!=3 ways;
1-2-5 --> 3!=6 ways;
1-3-4 --> 3!=6 ways;
2-2-4 --> 3!/2!=3 ways;
2-3-3 --> 3!/2!=3 ways.

Total of 3+6+6+3+3=21 ways.

Now, since the total number of outcomes is 6^3, then the probability is 21/6^3.

What is the probability that you will get a sum of 22 when you throw four dice simultaneously?

This sum of 22 can occur in the following cases:
6-6-6-4 --> 4!/3!=4 ways;
6-6-5-5 --> 4!/(2!2!)=6 ways.

Total of 4+6=10 ways.

Now, since the total number of outcomes is 6^4, then the probability is 10/6^4.

Hope it's clear.
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Re: What is the probability that you will get a sum of 8 when [#permalink]

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12 Dec 2015, 03:49
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: What is the probability that you will get a sum of 8 when   [#permalink] 12 Dec 2015, 03:49
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