Question

How many non-negative solutions are there for the equation $x+y+z=3?$

• A. $15$
• B. $10$
• C. $9$
• D. $5$

Answer 1

Answer: (B)

$10$

$x+y+z=3$

Non negative solutions

$(3,0,0)$

$(1,2,0)$

$(1,1,1)$

Are possible sets of solutions

Number of ways of arranging

$=\frac{3!}{2!}+3!+\frac{3!}{3!}=3+6+1=10$

Therefore there are $10$ possible ways