Mathematics - Permutation & Combination Question with Solution | TestHub

MathematicsPermutation & CombinationDivision of Identical itemsEasy2 minQB

MathematicsEasysingle choice

The number of point $(x, y, z)$ in space, whose each coordinate is a negative integer such that $x + y + z + 12 = 0$ , is :

Answer:

Solution:

$x + y + z + : 2 = 0, x, y, z$ are negative integers.

Let $x = - a, y = - b, z = - c, a, b, c$ are positive integers.

Then required number of points $(x, y, z)$

= number of positive integral solutions of $a + b + c = 12$

= coefficient of $x^{12}$ in $(x + x^{2} + \dots)^{3}$

Stream:JEESubject:MathematicsTopic:Permutation & CombinationSubtopic:Division of Identical items

⏱ 2mℹ️ Source: QB

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