Question

Number of solutions to $x+y+z=10$ where $1\le x,y,z\le 6$ is:

• A. $35$
• B. $36$
• C. $27$
• D. $66$

Answer 1

Answer: (C)

$27$

$x+y+z=10$ and $1\le x,y,z\le 6$ ..... $\left(i\right)$

$1$ $3$ $6$ $6$(No. of Possibilities)

$1$ $4$ $5$ $6$

$2$ $2$ $6$ $3$

$2$ $3$ $5$ $6$

$2$ $4$ $4$ $3$

$3$ $3$ $4$ $3$

Total $27$

Hence, number of solutions to $\left(i\right)$ is $27$.