A) 4
B) 6
C) 3
D) 5
Correct Answer: D
Solution :
There are two different families A and B with equal number of children. Let the children in each family be\[x.\] Thus the total number of children in both the families are\[2x\] Now, it is given that 3 tickets are distributed amongst the children of the families. And all the tickets are distributed to the children in family B Thus, the probability that all the three tickets go to the children in family B is given by \[\frac{1}{12}=\frac{{{\,}^{x}}{{C}_{3}}}{{{\,}^{2x}}{{C}_{3}}}\] On solving the above equation, we get, Thus,\[\frac{1}{12}=\frac{x(x-1)(x-2)}{2x(2x-1)(2x-2)}\] Thus, \[\frac{1}{6}=\frac{x-2}{2x-1}\] \[\to 3x-6=2x-1\] \[\to x=5\] Thus, the number of children in each family are 5.
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