FIND THE NUMBER OF NON-NEGATIVE INTEGRAL SOLUTIONS OF

2X+Y+Z=21

Dear Shaurya

2X+Y+Z=21    where X,Y,Z≥0

Y+Z =21-2X

   so          21  ≥  21-2X≥0

   so    10≥X≥0

So total number of solution   ^{21-2X +2-1}C_2-1

                                               =22-2X

but x varies from 0 to 10

so total solution   =x varies 0 to 10 ∑22-2X

                               =22*11 -2*55

                                =132