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FIND THE NUMBER OF NON-NEGATIVE INTEGRAL SOLUTIONS OF 2X+Y+Z=21

FIND THE NUMBER OF NON-NEGATIVE INTEGRAL SOLUTIONS OF


2X+Y+Z=21

Grade:12

1 Answers

Badiuddin askIITians.ismu Expert
148 Points
13 years ago

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 +2-1C2-1

                                               =22-2X

but x varies from 0 to 10

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

                               =22*11 -2*55

                                =132


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