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

Options

A. `44`
B. `55`
C. `66`
D. none of these

Answer

B

Explanation

`(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`