Find the number of positive integral triplet solutions such that:
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Go to the page in Wikipedia called 'Stars and Bars'. You might get the idea.
If you did not understand the wiki, then just understand this : You need to find the no. of ways you can partition 7 kinds of ( the binomial coefficient takes in account the solutions which include 0 as well, so since you want positive solutions, you subtract the no. of variables from your number) objects into groups of three. The Stars and Bars method is simply a generalization of that. n = 7 , k = 3