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Determine how many solutions there are to the equation \mathrm{x+y+z=12}, where \mathrm{\mathrm{x}, \mathrm{y}} and \mathrm{\mathrm{z}} are all \mathrm{\mathrm{W}}.

Option: 1

 66


Option: 2

77


Option: 3

 55


Option: 4

44


Answers (1)

best_answer

Given that \mathrm{x+y+z=12}

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=12}

The number of solutions is given as \mathrm{={ }^{12-1} C_{3-1}}
                                                          \mathrm{=^{11} C_{2}}
                                                          \mathrm{=55}

The correct option is (b)

Posted by

vishal kumar

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