Answer:
See explanation below.
Step-by-step explanation:
1) First let's take a look at the combinations that sum up 10:
- 1+3+ 6,
- 1+ 4+ 5,
- 2+2+6,
- 2+3+5,
- 2 + 4 + 4,
- 3+3+4
Notice that when we have 3 different numbers on the dice, we can permute them in 6 different ways. For example: Let's take 1 + 3 + 6, we can get this sum with these permutations:
1 + 3 + 6, 1 + 6 + 3, 3 + 6 + 1, 3 + 1 + 6, 6 + 1 + 3, 6 + 3 + 1.
And when we have two different numbers on the dice, we can permute them in 3 different ways:
2 + 2 + 6, 2 + 6 +2, 6 + 2 + 2.
So now we're going to write down the 6 combinations that sum up 10 but we're going to write down how many permutations of them we get:
- 1+3+ 6 : 6 permutations
- 1+ 4+ 5 : 6 permutations
- 2+2+6: 3 permutations
- 2+3+5: 6 permutations
- 2 + 4 + 4: 3 permutations
- 3+3+4: 3 permutations
Total of permutations: 6 + 6 + 3 + 6 + 3 + 3 =27.
Thus we have 27 different ways of getting a sum of 10.
2) Now we're going to take a look at the combinations that sum up 9 and we're going to proceed in a similar way:
- 1 + 2 + 6: 6 permutations
- 1+3+5: 6 permutations
- 1+4+4: 3 permutations
- 2+ 3+ 4: 6 permutations
- 2+2 +5: 3 permutations
- 3+3+3: 1 permutation.
Total of permutations: 6 + 6 + 3 + 6 +3 + 1 = 25.
Thus we have 25 different ways of getting a sum of 10
And we can conclude that the probability of getting a total of 10 is larger than the probability to get a total of 9.
