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The number of integral solutions of x+y+...

The number of integral solutions of `x+y+z=0` with `xgeq-5,ygeq-5,zgeq-5` is a. `134` b. `136` c. `138` d. `140`

A

135

B

136

C

455

D

105

Text Solution

Verified by Experts

The correct Answer is:
B
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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