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How many different combinations of outcomes can you make by [#permalink]
 21 Dec 2006, 18:34
Question Stats:
37% (02:16) correct
62% (00:37) wrong based on 2 sessions
How many different combinations of outcomes can you make by rolling three standard (6-sided) dice if the order of the dice does not matter?
(A) 24
(B) 30
(C) 56
(D) 120
(E) 216
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Re: PS_How many different ... [#permalink]
21 Dec 2006, 19:43
mm007 wrote: How many different combinations of outcomes can you make by rolling three standard (6-sided) dice if the order of the dice does not matter?
(A) 24
(B) 30
(C) 56
(D) 120
(E) 216
IMO Answer is E. 6*6*6 = 216 since order does not matter,
Last edited by 800_gal on 29 Dec 2006, 00:50, edited 1 time in total.
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Could someone explain please what is meant by" order doesn't matter" here?
also 3C3=1. So the combinations would be same in either case.
thanks a lot guys!
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C 56
I count all the possible combo.
definately not 6*6*6 since the question said 'order does not matters'.
It means we do not distinguish between (1,1,5) or (1,5,1) or (5,1,1) .All these are considered as 1 outcome.
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C. 56.
1) All dice have the same number:
you have 6 possibilities.
2) 2 dice have the same number, but the 3rd is different:
you have 6*5
3) 3 dice are all different:
you have 6*5*4/3! = 20.
Because the question says the order does not matter, u have to divide it by 3!.
so totally you have 56.
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Makes sense... Still getting confused with counting probs 
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Some further explanation on my answer above:
Case (2) is different from case (3).
In case 2, e.g. 5, (6, 6) and 6, (5, 5) are different.
However, in case (3), e.g. 2, 3, 4, and 4, 2, 3 are the same.
So, in case 2, you don't divide it by 2!, but in case (3), you divide it by 3!.
Case (2) is more of a permutation on itself.
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Re: How many different combinations of outcomes can you make by [#permalink]
09 Mar 2012, 03:14
mm007 wrote: How many different combinations of outcomes can you make by rolling three standard (6-sided) dice if the order of the dice does not matter?
(A) 24
(B) 30
(C) 56
(D) 120
(E) 216 The only way I can see this is 6*6*6 - 6 (same outcomes) ... Can anyone explain?
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Re: How many different combinations of outcomes can you make by [#permalink]
09 Mar 2012, 08:26
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rohitgoel15 wrote: mm007 wrote: How many different combinations of outcomes can you make by rolling three standard (6-sided) dice if the order of the dice does not matter?
(A) 24
(B) 30
(C) 56
(D) 120
(E) 216 The only way I can see this is 6*6*6 - 6 (same outcomes) ... Can anyone explain? If the order of the dice does not matter then we can have 3 cases: 1. XXX - all dice show alike numbers: 6 outcomes (111, 222, ..., 666); 2. XXY - two dice show alike numbers and third is different: 6*5=30, 6 choices for X and 5 choices for Y; 3. XYZ - all three dice show distinct numbers: C^3_6=20, selecting three different numbers from 6; Total: 6+30+20=56. Answer: C.
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Re: How many different combinations of outcomes can you make by
[#permalink]
09 Mar 2012, 08:26
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