Question

How many positive integral solutions are there for the equation $x+y+z=3$

• A. $15$
• B. $55$
• C. $10$
• D. $1$

Answer 1

The correct option is D $1$

Given $x+y+z=3$ $,$ $x,y,z>0$

Total combinations is given by ${}^{n-1}{C}_{r-1}$

Here, $n=3$ $,$ $r=3$

$\Rightarrow {}^{3-1}{C}_{3-1}={}^2{C}_2=1$ i.e. $(1,1,1)$

Hence, the answer is $1.$