IMPRESSIVE so what ARE the odds of rolling 35 on 12 dice?

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Posted by MathBArd on October 22, 2002 at 22:50:28:

In Reply to: AND HERE TIZZ: the full thing! posted by Denis Borris on October 22, 2002 at 18:54:17:

: The formula:
: Take 1 1 1 3 3 3 3 3 3 4 5 5 (one of 197 "number combos" that add up to 35)
: We have 3 of same, 6 of same, 1 of same, 2 of same:
: 12! / (3! * 6! * 1! * 2!) = 55440
: n! / [n(1)! * n(2)! ... * n(i)!]

: This is the results for ALL the sums:
: (columns: sums, number arrangements, total combos)
: 12/72 001 000000001
: 13/71 001 000000012
: 14/70 002 000000078
: 15/69 003 000000364
: 16/68 005 000001365
: 17/67 007 000004368
: 18/66 010 000012364
: 19/65 013 000031680
: 20/64 018 000074646
: 21/63 023 000163592
: 22/62 030 000336336
: 23/61 037 000653016
: 24/60 047 001203632
: 25/59 056 002115048
: 26/58 068 003555564
: 27/57 080 005734664
: 28/56 094 008895393
: 29/55 107 013297284
: 30/54 123 019188950
: 31/53 137 026771316
: 32/52 154 036154767
: 33/51 168 047315840
: 34/50 184 060060936
: 35/49 197 074005152
: 36/48 212 088573343
: 37/47 222 103027860
: 38/46 233 116523342
: 39/45 240 128184068
: 40/44 247 137194629
: 41/43 249 142891320
: 00042 252 144840476
: Total:2,176,782,336

: My program (half in English!):

: loop A from 1 to 6
: loop B from A to 6
: loop C from B to 6
: ...
: loop K from J to 6
: loop L from K to 6

: store above in array V(12) : V(1)=A, V(2)=B, ... V(12)=L
: X = A + B + C ... + K + L : get current sum
: W(X) = W(X) + 1 : update number for this sum in array W(72)

: (This section gets info for, and uses the formula)
: P = 1 : cumulative product of denominator
: N = 1 : number of "like numbers"
: loop M from 2 to 12 : to go thru array V(12)
: if V(M) = V(M-1) then N = N + 1 : update N and go to next loop
: else P = P * N! and N = 1 : update cumulative product
: endloop M
: P = P * N! : last portion up to M = 12

: Q = 12! / P : total combos for this number arrangement
: Y(X) = Y(X) + Q : update combos in array Y(72)

: Z = Z + Q : update grand total of combos; will end at 6^12

: endloops A-L

: Print arrays W(72) and Y(72) from 12 to 72
: (small sample:)
: 12 1 1
: 13 1 12
: ...
: 42 252 144840476
: ...
: 71 1 12
: 72 1 1

: Send this to Las Vegas? :)

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not very high..... Denis Borris 00:29:09 10/23/02 (0)

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Comments:
: : The formula: : : Take 1 1 1 3 3 3 3 3 3 4 5 5 (one of 197 "number combos" that add up to 35) : : We have 3 of same, 6 of same, 1 of same, 2 of same: : : 12! / (3! * 6! * 1! * 2!) = 55440 : : n! / [n(1)! * n(2)! ... * n(i)!] : : This is the results for ALL the sums: : : (columns: sums, number arrangements, total combos) : : 12/72 001 000000001 : : 13/71 001 000000012 : : 14/70 002 000000078 : : 15/69 003 000000364 : : 16/68 005 000001365 : : 17/67 007 000004368 : : 18/66 010 000012364 : : 19/65 013 000031680 : : 20/64 018 000074646 : : 21/63 023 000163592 : : 22/62 030 000336336 : : 23/61 037 000653016 : : 24/60 047 001203632 : : 25/59 056 002115048 : : 26/58 068 003555564 : : 27/57 080 005734664 : : 28/56 094 008895393 : : 29/55 107 013297284 : : 30/54 123 019188950 : : 31/53 137 026771316 : : 32/52 154 036154767 : : 33/51 168 047315840 : : 34/50 184 060060936 : : 35/49 197 074005152 : : 36/48 212 088573343 : : 37/47 222 103027860 : : 38/46 233 116523342 : : 39/45 240 128184068 : : 40/44 247 137194629 : : 41/43 249 142891320 : : 00042 252 144840476 : : Total:2,176,782,336 : : My program (half in English!): : : loop A from 1 to 6 : : loop B from A to 6 : : loop C from B to 6 : : ... : : loop K from J to 6 : : loop L from K to 6 : : store above in array V(12) : V(1)=A, V(2)=B, ... V(12)=L : : X = A + B + C ... + K + L : get current sum : : W(X) = W(X) + 1 : update number for this sum in array W(72) : : (This section gets info for, and uses the formula) : : P = 1 : cumulative product of denominator : : N = 1 : number of "like numbers" : : loop M from 2 to 12 : to go thru array V(12) : : if V(M) = V(M-1) then N = N + 1 : update N and go to next loop : : else P = P * N! and N = 1 : update cumulative product : : endloop M : : P = P * N! : last portion up to M = 12 : : Q = 12! / P : total combos for this number arrangement : : Y(X) = Y(X) + Q : update combos in array Y(72) : : Z = Z + Q : update grand total of combos; will end at 6^12 : : endloops A-L : : Print arrays W(72) and Y(72) from 12 to 72 : : (small sample:) : : 12 1 1 : : 13 1 12 : : ... : : 42 252 144840476 : : ... : : 71 1 12 : : 72 1 1 : : Send this to Las Vegas? :)

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