1.

Total number of integral solutions of the system of equations `x_(1)+x_(2)+x_(3)+x_(4)+x_(5)=20and x_(1)+x_(2)+x_(3)=5" when "x_(k)gel0,"is"`A. 335B. 336C. 338D. 340

Answer» We have, `x_(1)+x_(2)+x_(3)+x_(4)+x_(5)=20and x_(1)+x_(2)+x_(3)=5`
These two equtions reduce to
`x_(4)+x_(5)=15" "(i)`
and `x_(1)+x_(2)+x_(3)=5" "(ii)`
Since corresponding to each solution of (i) there are solutions of equation (ii). So, total number of solution of the given system of equations
= No. of solutions of (i) `xx` No. of solutions of (ii)
`=""^(15+2-1)C_(2-1)xx""^(5+3-1)C_(3)=""^(16)C_(1)xx""^(7)C_(2)=336`.


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