Question

3 dice are thrown. Find the number of ways such that sum on dice is n and n is 9,10 ,11, 12,13,14

Answer 1

There are 6^3 possible outcomes to rolling a die 3 times. Out of these, how many yield a total of (exactly) 10 dots?

First we find all sets {a,b,c} such that a+b+c=10

1, 3, 6
1, 4, 5
2, 3, 5


2, 2, 6
2, 4, 4
3, 3, 4

The total number of sets that fit these criteria is 6. If a≠b≠c, then there exist 3! unique permutations of {a,b,c}. If a=b≠c, then there exist 3 unique permutations of {a,b,c}- There cannot be a set such that a=b=c