Four persons are selected at random out of 3 men, 2 women and 4 children. The probability that there are exactly 2 children in the selection is

As there are 3 +2+4 = 9 persons


So, 4 persons out of 9 can be drawn in 9C4 ways = 126


Let E denote the event that there are exactly 2 children in the selection.


2children out of 4 can be selected in 4C2 = 6 ways


And rest two persons can be male or female. So we will select 2 persons out of remaining 5.


∴ P(E) =


Hence,


P(E) = 10/21


As our answer matches only with option (c)


∴ Option (c) is the only correct choice.

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