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anonymous
 one year ago
The number of ways in which we can get a score of 11 by throwing three dice is...
anonymous
 one year ago
The number of ways in which we can get a score of 11 by throwing three dice is...

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misty1212
 one year ago
Best ResponseYou've already chosen the best response.2you familiar with dice?

misty1212
 one year ago
Best ResponseYou've already chosen the best response.2ok i guess we got a bunch of counting to do then because you have 3 dice total, not the usual 2

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yep two dices would be easy.. but there's 3

misty1212
 one year ago
Best ResponseYou've already chosen the best response.2none of the dice can show a one, but if one shows a 2, then it can be \[(2,5,6)\] or any combination of those there are 6 i believe \[(2,5,6),(2,6,5),(5,2,6),(5,6,2),(6,2,5),(6,5,2)\] or \(3!=6\) ways where one is a two

anonymous
 one year ago
Best ResponseYou've already chosen the best response.018,27,45,56 are the options

misty1212
 one year ago
Best ResponseYou've already chosen the best response.2now lets move on to one showing a 3 \[(3,2,6)\] 6 of those \[(3,3,5)\] 3 of those \[(3,4,4)\] 3 of those guess that is it for one of them showing a 3

misty1212
 one year ago
Best ResponseYou've already chosen the best response.2ready to move on to 4? we have to make sure we don't count anything twice

misty1212
 one year ago
Best ResponseYou've already chosen the best response.2oh i made a mistake one could show a 1 lets count those too

misty1212
 one year ago
Best ResponseYou've already chosen the best response.2\[(1,5,5)\] 3 of those and \[(1,4,6)\] 6 of those

misty1212
 one year ago
Best ResponseYou've already chosen the best response.2keep counting in this way, you will get it

misty1212
 one year ago
Best ResponseYou've already chosen the best response.2oh nvm we are done just count them up

misty1212
 one year ago
Best ResponseYou've already chosen the best response.2for two dice the pattern is \[1,2,3,4,5,6,5,4,3,2,1\]

misty1212
 one year ago
Best ResponseYou've already chosen the best response.2yeah count the number of ways for each for 3 dice the pattern is \[1,3,6,10,15,21,25,27,27,25,21,15,10,6,3,1\]

misty1212
 one year ago
Best ResponseYou've already chosen the best response.2for rolling respectively \[3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18\]

misty1212
 one year ago
Best ResponseYou've already chosen the best response.2notice that \[(1,4,6)\] where all the numbers are different has \(3!=6\) possible ways to do it

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0its confusing in counting cases

misty1212
 one year ago
Best ResponseYou've already chosen the best response.2whereas \((1,5,5)\) has only 3 possible ways \[(1,5,5),(5,1,5),(5,5,1)\]

misty1212
 one year ago
Best ResponseYou've already chosen the best response.2you got one possibility is \((1,4,6)\) right because they add up to 11

misty1212
 one year ago
Best ResponseYou've already chosen the best response.2but you have \(3!=6\) permutations of those three numbers

misty1212
 one year ago
Best ResponseYou've already chosen the best response.26 is not so big that we cannot list them \[(1,4,6),(1,6,4),(4,1,6),(4,6,1),(6,1,4),(6,4,1)\] six ways to do it

misty1212
 one year ago
Best ResponseYou've already chosen the best response.2so lets do them in order

misty1212
 one year ago
Best ResponseYou've already chosen the best response.2\[(1,4,6)\] 6 choices \[(1,5,5)\] 3 choices

misty1212
 one year ago
Best ResponseYou've already chosen the best response.2\[(2,3,6)\] 6 choices \[(2,4,5)\] 6 choices

misty1212
 one year ago
Best ResponseYou've already chosen the best response.2\[(3,3,5)\]3 choices \[(3,4,6)\] 6 choices

triciaal
 one year ago
Best ResponseYou've already chosen the best response.0dw:1433100469127:dw

misty1212
 one year ago
Best ResponseYou've already chosen the best response.2and that is all if you go further, you will get repeats

misty1212
 one year ago
Best ResponseYou've already chosen the best response.2add to get \[6+3+6+6+3+6=27\]

triciaal
 one year ago
Best ResponseYou've already chosen the best response.0my approach here is to find the possibilities of getting 11 when the first die is a 1 then when a 2 etc eventually will add the possibilities

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0great @misty1212 thanks @triciaal

misty1212
 one year ago
Best ResponseYou've already chosen the best response.2\[\color\magenta\heartsuit\]

triciaal
 one year ago
Best ResponseYou've already chosen the best response.0dw:1433101773240:dw

triciaal
 one year ago
Best ResponseYou've already chosen the best response.0I see 2 errors P(2) = 4 and P(6) = 8
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