Probability Ques 27
Question-
A team of 6 persons is to be selected from a group of 3 men, 3 women and 4 children. What is the probability that it comprises of exactly 2 children?
(1) $\frac{1}{35}$
(2) $\frac{1}{10}$
(3) $\frac{3}{70}$
(4) $\frac{3}{7}$
(5) $\frac{5}{7}$
(IBPS Bank PO/MT CWE (Main Exam) 26.11.2017)
Show Answer
Correct Answer: (4)
Solution: (4)
Total number of persons $=3+3+4=10$
Total number of ways of selecting 6 out of 10 persons $={ }^{10} C_{6}=\frac{10 !}{6 ! 4 !}=\frac{10 \times 9 \times 8 \times 7}{4 \times 3 \times 2}$ $=210$
Number of ways 2 children can be selected out of 4 $={ }^{4} C_{2}=\frac{4 \times 3}{2}=6$
Number of ways remaining 4 persons can be selected out of
$6={ }^{6} C_{4}=\frac{6 !}{4 ! 2 !}$
$\therefore$ Required probability $=\frac{6 \times 15}{210}=\frac{3}{7}$
BETA
