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Find number of negative integral solutio...

Find number of negative integral solution of equation `x + y + z = - 12`

A

`44`

B

`55`

C

`66`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
`(b)` `x+y+z=-12`
Here `-10 le x`, `y`, `z le -1`
Let `x_(1)=-x`, `y_(1)=-y`, `z_(1)=-z`
`:.` we have `x_(1)+y_(1)+z_(1)=12` , where `1 le x_(1)`, `y_(1)`, `z_(1) le 12`
`:.` Number of solutions of the equation
`=^(12-1)/(C_(3-1)=^(11)C_(2)=55`
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