1.

The number of integral solutions of `x+y+z=0`with `xgeq-5,ygeq-5,zgeq-5`isA. 135B. 136C. 455D. 105

Answer» Let `u=x+5,v=y+5andw=z+5`. Then, `u,v,wge0andx+y+z=0impliesu+v+w=15`.
The number of solutions of this equation is
`""^(15+3-1)C_(3-1)=""^(17)C_(2)=136`


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