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  • The number of positive integral solutions for the equation <img alt="\mathrm{p+q+r+s+t=15}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7Bp&plus;q&plus;r&plus;s&

The number of positive integral solutions for the equation \mathrm{p+q+r+s+t=15} is 

Option: 1

760


Option: 2

560


Option: 3

 1001


Option: 4

1008


Answers (1)

best_answer

Given that
\mathrm{p+q+r+s+t=15}
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{p+q+r+s+t=15}

The number of solutions is given as \mathrm{={ }^{15-1} C_{5-1}}
                                                         \mathrm{=^{14} C_{4}}
                                                         \mathrm{=1001}

The correct option is (c)

Posted by

Ritika Harsh

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