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  • Determine the number of solutions to the problem <img alt="\mathrm{i+j+k+l+m=33}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7Bi&plus;j&plus;k&plus;l&plus;m%3D33

Determine the number of solutions to the problem \mathrm{i+j+k+l+m=33}, where \mathrm{\mathrm{i}, \mathrm{j}, \mathrm{k}, \mathrm{l}} and \mathrm{\mathrm{m}} belong to \mathrm{\mathrm{W}}.

Option: 1

35960


Option: 2

76540


Option: 3

98120


Option: 4

24680


Answers (1)

best_answer

Given that \mathrm{i+j+k+l+m=33}

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=33}

The number of solutions is given as

\mathrm{={ }^{33-1} C_{5-1}}
\mathrm{={ }^{32} C_{4}}
\mathrm{=35960}

The correct option is (a)

 

 

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chirag

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