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  • The number of triplets (x,y,z), where x, y, z are distinct non negative integers satisfying x + y + z = 15, is :Option: 1 136<div class

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

Option: 1

136


Option: 2

114


Option: 3

80


Option: 4

92


Answers (1)

best_answer

x+y+z=15 \text { Total no. solution }={ }^{15+3-1} C_3=136 \ldots Let x=y \neq z \begin{aligned} & 2 \mathrm{x}+\mathrm{z}=15 \Rightarrow \mathrm{z}=15-2 \mathrm{t} \\ & \Rightarrow \mathrm{r} \in\{0,1,2, \ldots 7\}-\{5\} \end{aligned}


7 solutions

there are 21 solutions in which exactly
Two of x, y, z are equal ... (2)
There is one solution in which x = y = z ... (3)
Required answer = 136 – 21 – 1= 144

Posted by

Shailly goel

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