Q 23 Four persons are to be chosen at random from a group of 3 men, 2 women and - Maths - Probability

Question

Q 23 Four persons are to be chosen at random from a group of 3 men,
2 women and 4 children Find the probability of selecting
(i) 1 man, 1 woman and 2 children
(ii) Exactly 2 children

Shruti Tyagi · Accepted Answer

Dear student,

(i) No
 of ways of selecting 4 person=C49=9!4!×5!=9×8×7×6×5!4×3×2×5! =3×2×7×3=126 waysWays of selecting 1 man=C13=3!1!×2!=3×2!1×2!=3similarly,Ways of selecting 1 woman=C12=2Ways of selecting 2 children=C24=4!2!×2!=4×3×2!2×2!=6∴Probability of selecting 1 man,  1 woman, 4 children=Ways of selecting 1 man×Ways of selecting 1 woman×Ways of selecting 2 childrenTotal no
 of ways=3×2×6126=621=27⇒Probability of selecting 1 man,  1 woman, 2 children=27
(ii) We have,
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Regards

Q.23. Four persons are to be chosen at random from a group of 3 men, 2 women and 4 children. Find the probability of selecting (i) 1 man, 1 woman and 2 children (ii) Exactly 2 children

Q.23. Four persons are to be chosen at random from a group of 3 men, 2 women and 4 children. Find the probability of selecting
(i) 1 man, 1 woman and 2 children
(ii) Exactly 2 children