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Find the number of solutions of (5+2)(p+q+r)=14 , such that p , q and r are odd numbers

Option: 1

3


Option: 2

6


Option: 3

2


Option: 4

5


Answers (1)

best_answer

Given,
\begin{aligned} &(5+2)(p+q+r)=14 \text { and }\\ &p, q, r>0 \end{aligned}
Generalized formula to find the number of solutions of equations is
a_1+a_2+\ldots . .+a_r=(n+r-1) c_{r-1} $$ Let, $p=p, q=q, r=r Then, $p+q+r=2
So the equation becomes
p + q + r = 2
Hence from above equation, n = 2 and r = 3
Hence the total number of solutions =(2+3-1) c_{3-1}=4 c_2=6

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