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# Two persons A and B have equal number of sons. There are three cinema tickets which are to be distributed among the sons of A and B. The probability that all the tickets go to sons of A is $\large\frac{1}{20}$. The number of sons each of them is :

$\begin {array} {1 1} (1)\;3 & \quad (2)\;4 \\ (3)\;5 & \quad (4)\;6 \end {array}$

Lt each have $x$ rows
$\therefore$ Probability that all the tickets go to the rows of A = $\large\frac{xc_3}{2xc_3}$
$\Rightarrow \large\frac{x(x-1)(x-2)}{2x(2x-1)(2x-2)}= \large\frac{1}{20}$
$\Rightarrow x = 3$
Ans : (1)