Question

Find the number of non negative integral solutions of equation $a+b+c+d=20$.

• A. $1800$
• B. $1771$
• C. $1770$
• D. None of the above.

Answer 1

The correct option is B

$1771$

Explanation for the correct option:

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

Let, $a_1+a_2+a_3+a_4=x$ is an equation.

Therefore, the number of non-negative integral solutions in this equation

$=C_{n-1}^{x+n-1}$, where $n=$number of terms in that equation.

Here, $n=4,x=20$.

Step:2 Calculating the number of non-negative integral solutions.

$$\begin{gathered} =C_{n-1}^{x+n-1} \\ =C_{4-1}^{20+4-1} \\ =C_3^{23} \\ =\frac{23!}{3!\times 20!} \\ =\frac{23\times 22\times 21\times 20!}{3\times 2\times 20!} \\ =1771 \end{gathered}$$

Hence, Option(B) is the correct answer.