How many natural number solutions are possible for equation below ?
x + y +z + w = 20

^{23} C_{3}

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^{22} C_{2}

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^{19} C_{3}

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None of these

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Solution

The correct option is C $^{19} C_{3}$
In this case partion rule is applicable, such that each of x, y, z and w should get at least one thing.

hence no. of ways
$=^{20 - 1} C_{4 - 1} =^{19} C_{3}$

Hence option (c)

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