30 Show that the odds against at least one 1 appearing in a

30. Show that the odds against at least one 1 appearing in a throw of three dice is 125 : 91. (This answer was stated by Cardano.)

There are 216 possible combinations of 3 dice that are rolled. (6 raised to the 3rd power.)

91 out of those 216 combinations include at least one \"1\". 125 out of those 216 combinations do NOT contain any \"1\".

Hence, there odds against rolling a \"1\" with 3 dice are 125 to 91.