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# can someone explain why you won't count 3-3 and 3-3 twice for dice?

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Intern
Joined: 23 Jul 2015
Posts: 34
can someone explain why you won't count 3-3 and 3-3 twice for dice?  [#permalink]

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17 Nov 2015, 22:28
For example what is the chances John will roll a 6 by rolling two dice?
There are 36 outcomes and according to text 5 ways to roll a 6: 5-1, 1-5, 2-4, 4-2 and 3-3.
Why won't you count 3-3 and 3-3 like you do with 5-1 and 1-5?
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can someone explain why you won't count 3-3 and 3-3 twice for dice?  [#permalink]

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17 Nov 2015, 23:35
You can distinguish between 5,1 and 1,5. Say, in the first throw we got Dice 1 = 5 and Dice 2 = 1 and in the second throw we got Dice 1 = 1 and Dice 2 = 5. Here, even though the outcome is 6, we have two different ways to get 6. (2!/1 = 2)

But when we get Dice 1 = 3 and Dice 2 = 3 in both the throws, there isn't any significant difference between the two throws and the second throw can be considered as a repetition of the 1st throw. We can interpret this as 2!/2 = 1. So there is only 1 way when both the dices show up the same number.
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Re: can someone explain why you won't count 3-3 and 3-3 twice for dice?  [#permalink]

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18 Nov 2015, 15:43
1
Hi jasonfodor,

When rolling 2 dice, there are (6)(6) = 36 possible outcomes (including many 'duplicate' totals). They are...

11
12
13
14
15
16

21
22
23
24
25
26

31
32
33
34
35
36

41
42
43
44
45
46

51
52
53
54
55
56

61
62
63
64
65
66

The reason why you could 3-3 just once is BECAUSE it appears just once.

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Re: can someone explain why you won't count 3-3 and 3-3 twice for dice?  [#permalink]

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19 Aug 2017, 22:45
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Re: can someone explain why you won't count 3-3 and 3-3 twice for dice?   [#permalink] 19 Aug 2017, 22:45
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