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  • Determine the number of solutions to the problem <img alt="\mathrm{i+j+k+l+m=45}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7Bi&plus;j&plus;k&plus;l&plus;m%3D45

Determine the number of solutions to the problem \mathrm{i+j+k+l+m=45}, where \mathrm{\mathrm{i}, \mathrm{j}, \mathrm{k}, \mathrm{l}} and \mathrm{\mathrm{m}} belong to \mathrm{\mathrm{W}}.

Option: 1

345675


Option: 2

276565


Option: 3

213589


Option: 4

271502


Answers (1)

Given that \mathrm{i+j+k+l+m=45}
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{i+j+k+l+m=45}

The number of solutions is given as \mathrm{={ }^{12-1} C_{3-1}}
                                                          \mathrm{={ }^{45-1} C_{5-1}}
                                                          \mathrm{={ }^{44} C_{4}}
                                                          \mathrm{=271502}

The correct option is (d)

Posted by

Sumit Saini

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