Assume all the numbers are natural numbers (positive integers, excluding zero).
If the first number is 1, the other two numbers must add up to 23, for example, 1+2+21=24.
The second number can go up to 11 making the third number 12. So if 1 is the first number then there are 10 possible combinations:
1+2+21=1+3+20=1+4+19=...1+11+12=24.
Now start with number 2. This makes the second number run between 3 and 10, for example, 3+10+11=24. 8 combinations.
For 3 there are 7; for 4, 5; for 5, 4; for 6, 2 (they are: 6+7+11=24, 6+8+10=24, 6+9+9 repeats 9 so we can't count it; for 7 there's only 7+8+9=24.
Add all these counts: 10+8+7+5+4+2+1=37 combinations.
If permutations are allowed, that is, we include sums like 7+14+3, which is the same as 3+7+14 then we multiply 37 by 6=222 permutations, because there are 6 ways to arrange three different numbers.