Question

The number of solutions of the equation $x+y+z=10$ in positive integers $x,y,z$ is equal to

• A. 36
• B. 55
• C. 72
• D. 45

Answer 1

Answer: (A)

Given equation, is $x+y+z=10$
where, $x,y$ and $z$ are positive integers.
$\therefore$ Required number of solutions $={}^{(10-1)}{C}_{(3-1)}$
$={}^9{C}_2=\frac{9\times 8}{2}=36$