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Question

Let M be the maximum value of the product of two positive integers when their sum is 66. Let the sample space $S = \left\{ {x \in \mathbb{Z}:x(66 - x) \ge {5 \over 9}M} \right\}$ and the event $\mathrm{A = \{ x \in S:x\,is\,a\,multiple\,of\,3\}}$. Then P(A) is equal to :

$\frac{1}{3}$
$\frac{1}{5}$
$\frac{7}{22}$
$\frac{15}{44}$

Solution

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