Question

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

Answer 1

Answer: (D)

3

Answer 2

Let each of the friend have x daughters. Then the probability that all the tickets go to the daughters of A is $\frac { { } ^ { \mathrm { x } } \mathrm { C } _ { 3 } } { { } ^ { 2 \mathrm { x } } \mathrm { C } _ { 3 } }$ . Therefore $\frac { { } ^ { \mathrm { x } } \mathrm { C } _ { 3 } } { { } ^ { 2 \mathrm { x } } \mathrm { C } _ { 3 } } = \frac { 1 } { 20 } \Rightarrow \mathrm { x } = 3$