The number of integral solutions for the equation $x + y + z + t = 20$ where $x, y, z, t$ are all $\geq - 1$ is

^{20} C_{4}

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^{23} C_{3}

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27 C_{4}

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^{27} C_{3}

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Solution

The correct option is A $^{23} C_{3}$
$x + y + z + t = 20$
And $x, y, z, t \geq - 1$
According to $x_{1} + x_{2} + x_{3} + . . . . . . . . x_{r} = n$
Number of non negative integral solutions $=^{n + r - 1} C_{r - 1}$
$\Rightarrow^{23} C_{3}$

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