Solutions

Find the number of positive integral triplet solutions ( x , y , z ) (x,y,z) such that: x + y + z = 10 \large x+y+z=10

36 121 1000-10 ( 10 3 ) ( 10 2 ) \binom{10}{3}-\binom{10}{2}

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1 solution

Rajdeep Ghosh
May 17, 2017

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 n=7 , k=3

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