Question

Find the number of non-negative integral solutions of equation $x+y+z=10$.

• A. $C_2^{10}$
• B. $C_2^{12}$
• C. $C_2^{11}$
• D. $C_2^9$

Answer 1

The correct option is B

$C_2^{12}$

Explanation for correct option:

Step:1 Derive the general form of non-negative integral solutions in an equation.

Given equation is $x+y+z=10$

$=C_{n-1}^{a+n-1}$

Here, $n=3,a=10$.

Step:2 Equating the number of non-negative integral solutions

$$\begin{gathered} =C_{n-1}^{a+n-1} \\ =C_{3-1}^{10+3-1} \\ =C_2^{12} \end{gathered}$$

Hence, Option(B) is the correct answer.