The number of triplets (x, y, z). where x, y, | vedclass

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Question

$x+y+z=15$

Total no. of solution $={ }^{15+3-1} C _{3-1}=136$

Let $x = y 
eq z$

$2 x + z =15 \Rightarrow z =15-2 t$

$\Rightarrow r \in\{0

Vedclass · Accepted Answer

$114$

Vedclass · Answer

$x+y+z=15$

Total no. of solution $={ }^{15+3-1} C _{3-1}=136$

Let $x = y 
eq z$

$2 x + z =15 \Rightarrow z =15-2 t$

$\Rightarrow r \in\{0,1,2, \ldots 7\}-\{5\}$

$	herefore 7 	ext { solutions }$

$	herefore 7$ solutions

$	herefore$ there are 21 solutions in which exactly

Two of $x _1 y _1 z$ are equal

There is one solution in which $x=y=z$

Required answer $=136-21-1=114$

The number of triplets $(x, y, z)$. where $x, y, z$ are distinct non negative integers satisfying $x+y+z=15$, is

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