Two friends A and B have equal number of daughters. There are three cinema tickets which are to be d

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14.Probability

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Two friends $A$ and $B$ have equal number of daughters. There are three cinema tickets which are to be distributed among the daughters of $A$ and $B$. The probability that all the tickets go to daughters of $A$ is $1/20$. The number of daughters each of them have is

A

$4$

B

$5$

C

$6$

D

$3$

Solution

(d) Let each of the friend have $x$ daughters.

Then the probability that all the tickets go to the daughters of $A$ is $\frac{{{}^x{C_3}}}{{{}^{2x}{C_3}}}.$

Therefore $\frac{{{}^x{C_3}}}{{{}^{2x}{C_3}}} = \frac{1}{{20}} \Rightarrow x = 3.$

Standard 11

Mathematics

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