Three dice are rolled. What is the probability of sum of the numbers on the faces being 10?

• To be able to roll a 10 with 3 dice, the first 2 dice must give a value between 4 and 9 (probability of 3/4), in which
  case there is a 1/6 chance that the third die will make the total 10. So, the overall probability is 3/4*1/6=1/8
• 9 years agoHelpfull: Yes(2) No(2)
• 1---6 3
  5 4
  2---5 3
  3,4,5,6 are used above so no need to take again we can get from combinations of above 3 = 3!+3!+3!(3 different numbers arranging in order)
  = 18
  two numbers can repeat so 442,226,334
  so no. of arrangements=3!/2! + 3!/2! + 3!/2! = 9
  so probability to get sum 10 is
  = (18+9)/(6*6*6)
  = 1/8
• 9 years agoHelpfull: Yes(1) No(2)
• The combination of 10 can occur when we have (1,3,6) (1,4,5) (2,2,6) (2,3,5) (2,4,4) , (3,3,4) = 6 patterns.
  (1,3,6) can be 1,3,6 or 1,6,3 or 3,1,6 or 3,6,1 or 6,1,3 or 6,3,1 that is in 3! ways .
  Set having repeating digits like 2,2,6 can be ordered in 3!/2 ways = 3 ways (like 2,2,6 or 2,6,2 or 6,2,2)
  Hence over all occurrences = 6 + 6 + 3 + 6 + 3 + 3 = 27 ways.
  Probability = 27/216 = 3/24 = 1/8
• 6 years agoHelpfull: Yes(1) No(0)