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Find the number of non-negative intergal...

Find the number of non-negative intergal solution of the equation `x+y+z=7`

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The number of ways is equal to the coefficient of `x^(7)` in the expansion `(1+x+x^(2)+x^(3)+x^(4)…………..)^(3)`
=coefficient of `x^(7)` in `((1)/(1-x))^(3)`
=coefficient of `x^(7)` in `(1-x)^(-3)`
=coefficient of `x^(7)` in `(1+""^(3)C_(1)x+ ^(4)C_(2)x^(2)+^(5)C_(3)x^(3)+^(6)C_(4)x^(4)x^(7)C_(5)x^(5)+^(8)C_(6)x^(6)+^(9)C_(7)x^(7)+.........)`
`=""^(9)C_(7)=(9!)/(2!7!)`
`=(9xx8)/(2)=36`
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