THE NUMBER OF ORDERED TRIPLETS OF POSITIVE INTEGERS WHICH ARE SOLUTIONS OF THE EQUATION X+Y+Z=100

Dear shaurya

X+Y+Z=100  where X≥1 ,Y≥1,Z≥1

let U =X-1

    V=Y-1

  W=Z-1

             where U≥0,V≥0,W≥0

 now equation become

 U+V+W =97

Now the total number of solution is   ^{97 +3-1}C_3-1

                                                          =⁹⁹C₂