A teacher takes three children from her class to a zoo at a time, but she does not take the same three children to the zoo more than once. She finds that she went to the zoo 84 times more than a particular child has gone to the zoo. The number of children in her class is

The number of times the teacher goes to the zoo is  nC3. The number of times a particular child goes to the zoo is equal to number of ways two other children can be selected who accompany a particular child, i.e.,  n−1C2. From the question.    nC3−n−1C2=84 or     (n−1)(n−2)(n−3)=6×84=9×8×7⇒    n−1=9