Question 1092332
<br>You will need to re-post, describing the constraints clearly.<br>
When I picture this problem, the model I like to use is dividing pieces of candy among children.  So your problem is to find the number of ways of dividing 174 pieces of candy among 6 children.  Then you need to clarify several points about your question:<br>
(1) Presumably, all the numbers have to be whole numbers (you can't give fractions of pieces of candy to any child).  (If this were not the case, there would clearly be an infinite number of ways to choose 6 numbers that add to 174.)
(2) Can 0 be used? (Can the candy be distributed so that one or more of the children don't get any?)
(3) Does the order matter? or are you in fact looking for, as you say, combinations and not permutations.  For example, are 174+0+0+0+0+0 and 0+0+0+0+0+174 the same solution, or different solutions?  (is giving all the candy to one child the same, or a different, solution than giving all the pieces to a different child?)
(4) Can any of the numbers be used more than once? (Can more than one child get a particular number of candies? or does each child have to get a different number?)
(5) Is there a restriction on how big any one of the numbers can be? (Is there a limit to how many pieces of candy any one child can get?)<br>
There might be other considerations that I haven't mentioned above....<br>
I can tell you that there is a single straightforward computation that can be made if (1) all numbers must be whole numbers; (2) 0 can be used; (3) order DOES matter; (4) numbers can be used more than once; and (5) there is no restriction on how large any of the numbers can be.<br>
The same computation can be used with very slight modification if all of the numbers must be positive (0 not allowed).<br>
If you have any of the other restrictions mentioned above, the process for finding the answer becomes far more complicated.<br>
I hope this response helps you toward eventually getting an answer to your question.