Four people are chosen at random from a group of 3 men, 2 women and 4 children. The probability that exactly 2 of them are children is:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \(\frac{10}{21}\)
The probability is the number of favourable selections divided by the number of all possible selections. The order in which people are picked does not matter, so both are counted with combinations.
The group has \(3+2+4=9\) people, so 4 of them can be chosen in \({}^{9}C_{4}=126\) ways
Two children and no more: the 2 children come from the 4 children in \({}^{4}C_{2}=6\) ways
The other 2 must be adults, chosen from the 5 adults (3 men + 2 women) in \({}^{5}C_{2}=10\) ways
Favourable selections \(=6\times10=60\)
Probability \(\displaystyle =\frac{60}{126}=\frac{10}{21}\)