The number of positive integral solutions of the equation x + y + z = 12

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Solution

The correct option is B 55
$x + y + z = 12$
$∴^{12 - 1} C_{3 - 1} =^{11} C_{2} = \frac{11.10}{2} = 55$

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x + y + z = - 12

x + y + z + w = 20

x + y + z = - 12

Δ = 12

Δ = ∣ ∣ ∣ ∣ \begin{matrix} y + z & z & y z & z + x & x y & x & x + y \end{matrix} ∣ ∣ ∣ ∣ = 0

x + y + z + w = 19,

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