Q. A class of twelve children has two more boys than girls. A group of three children are randomly picked from this class to accompany the teacher on a field trip. What is the probability that the group accompanying the teacher contains more girls than boys?
Ans: Option B
Sol:
∵B=G+2 and B+G=12 ⇒ B=7, G=5
Total ways of picking 3 children = 12C3
Favourable ways (when No. of girls are > No. of Boys)
= Either (2G and 1B) or (3G)
=( 5C2 × 7C1)+ 5C3=10×7+10=80
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