Part a)
The different number combinations that will total 9:
1-2-6
1-3-5
1-4-4
2-2-5
2-3-4
3-3-3
Those that have 3 different values (like 1-2-6) have 6 different ways to get that combination.
Those that have 2 different values (like 1-4-4) have 3 different ways to get that combination.
Those that have only 1 way (like 3-3-3) have only 1 way to get that combination.
Thus, there will be 6 + 6 + 3 + 3 + 6 + 1 = 25 ways.
One way to determine the number of ways to get a particular combination is to use factorials.
The numerator is the factorial of the number of dice: 3!.
This numerator is divided by the factorial of each different number used -- for instance:
If the values used are 2-3-4: 3! / (1!·1!·1!) because each number is used once = 6.
If the values used are 2-2-5: 3! / (2!·1!) because the 2 is used twice and the 5 is used once = 3.
If the values used are 3-3-3: 3! / (3!) because the 3 is used three times.
