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  • Determine how many solutions there are to the equation ,where 

Determine how many solutions there are to the equation \mathrm{x+y+z=17},where  \mathrm{\mathrm{x}, \mathrm{y}}, and \mathrm{\mathrm{z}} are all \mathrm{\mathrm{W}}.

Option: 1

120


Option: 2

240


Option: 3

360


Option: 4

480


Answers (1)

best_answer

Given that \mathrm{x+y+z=17}

For \mathrm{x_{1}+x_{2}+x_{3}+\ldots \ldots x_{r}=n}

The number of solutions will be \mathrm{={ }^{(n-1)} C_{(r-1)}}

Then for \mathrm{x+y+z=17}

The number of solutions is given as \mathrm{={ }^{17-1} C_{3-1}}
                                                          \mathrm{=^{16} C_{2}}
                                                          \mathrm{=120}

The correct option is (a)

Posted by

Divya Prakash Singh

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