KCC's Quizzes AQQ287 about throwing 3 dice

1) Enumeration of the results of each throw gives:
    1 way  for 3
    3 ways for 4
    6 ways for 5
    10 ways for 6
    15 ways for 7
    21 ways for 8
    25 ways for 9
    27 ways for 10
    27 ways for 11
    25 ways for 12
    21 ways for 13
    15 ways for 14
    10 ways for 15
    6 ways for 16
    3 ways for 17
    1 ways for 18
Two numbers, 10 and 11, have the highest count of 27 so they have the highest chance of occurring. P(S) => 27/216=0.125

2) For n dice the number(s) with the highest count is(are) at the mid range of S. This gives the most range of selection to equal S.
   Min count = n, Max count = 6n
   Mid range => (6n-n)/2 + n = 3.5n
   S = floor(3.5n) and ceil(3.5n); Both numbers are equal when n is an even integer.
   Example: S=7 for 2 dice and S=10 and 11 for 3 dice.

1) Enumeration of the results of each throw gives:
    1 way  for 3
    3 ways for 4
    6 ways for 5
    10 ways for 6
    15 ways for 7
    21 ways for 8
    25 ways for 9
    27 ways for 10
    27 ways for 11
    25 ways for 12
    21 ways for 13
    15 ways for 14
    10 ways for 15
    6 ways for 16
    3 ways for 17
    1 ways for 18
Two numbers, 10 and 11, have the highest count of 27 so they have the highest chance of occurring. P(S) => 27/216=0.125

2) For n dice the number(s) with the highest count is(are) at the mid range of S. This gives the most range of selection to equal S.
   Min count = n, Max count = 6n
   Mid range => (6n-n)/2 + n = 3.5n
   S = floor(3.5n) and ceil(3.5n); Both numbers are equal when n is an even integer.
   Example: S=7 for 2 dice and S=10 and 11 for 3 dice.

Excellent retiredEE  and with a solid and clear development, congratulations!