The number of non-negative integral solutions of $\mathrm{x}_1+\mathrm{x}_2+\mathrm{x}_3+\mathrm{x}_4=10$ is
The number of non-negative integral solutions of $\mathrm{x}_1+\mathrm{x}_2+\mathrm{x}_3+\mathrm{x}_4=10$ is
- $120$
- $144$
- $256$
- $286$
Solution
Given $x_1+x_2+x_3+x_4=10$
Now non-negative solution
$\begin{aligned}
& ={ }^{10+4-1} C_{4-1} \\
& ={ }^{13} C_3=\frac{13 \times 12 \times 11}{3 \times 2}=286
\end{aligned}$
Asked in: AP EAMCET 2023 (15 May Shift 2)
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