Probability Ques 45
Question-
A committee of 4 people is to be formed from 3 men, 2 women and 4 children. What is the probability that exactly two of chosen people are children?
(1) $\frac{11}{15}$
(2) $\frac{12}{17}$
(3) $\frac{10}{21}$
(4) $\frac{15}{19}$
(5) $\frac{20}{27}$
(IBPS Bank PO/MT CWE Prelim Exam, 03.10.2020)
Show Answer
Correct Answer: (3)
Solution: (3)
Total possible outcomes $=$ selection of 4 persons out of 9 persons $={ }^{9} C_{4}$
2 children should be there and rest 2 person are to be selected from ( 2 women +3 men) 5 people.
Favourable outcomes $={ }^{4} C_{2} \times{ }^{5} C_{2}$
$\therefore \quad$ Required probability $=\frac{{ }^{4} C_{2} \times{ }^{5} C_{2}}{{ }^{9} C_{4}}$
$=\left(\frac{4 \times 3}{2 \times 1} \times \frac{5 \times 4}{2 \times 1}\right) \div \frac{9 \times 8 \times 7 \times 6}{4 \times 3 \times 2 \times 1}$
$=60 \div(14 \times 9)=\frac{60}{14 \times 9}=\frac{10}{21}$
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