Question
Four persons are chosen at random from a group of 3 men , 2 women and 4 children . The chance that exactly 2 of them are children is :
Answer: Option D
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Let S be the sample space and E be the even of choosing four persons such that 2 of them are children .Then,
n (S) = number of ways of choosing 4 persons out of 9 .
= `9_ (C_4) = ((9 xx 8 xx 7 xx 6))/((4 xx 3 xx 2 xx 1))` = 126.
n(E) = Number of ways of choosing 2 children out of 4 and 2 persons out of (3 + 2) persons .
= `(4_(C_2) xx 5_(C_2)) = ((4 xx 3))/((2 xx 1)) xx ((5 xx 4))/(2 xx 1))` = 60.
`:.` P(E) = `(n(E))/(n(S)) = 60/126 = 10/21`
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