Question

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 $84$ number of times more than a particular child has gone to the zoo. The number of children in her class is

• A. $12$
• B. $10$
• C. $60$
• D. None of these

Answer 1

The correct option is B $10$

The number of times the teacher goes to the zoo is ${}^n{C}_3$. 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., ${}^{n-1}{C}_2$. From the question, ${}^n{C}_3{-}^{n-1}{C}_2=84$
or
$(n-1)(n-2)(n-3)=6\times 84=9\times 8\times 7\Rightarrow n-1=9$.