Q: A teacher takes 3 children from her class to the zoo at a time as often as she can , but she does not take the same three children to the zoo more than once. She finds that she goes to the zoo 84 times more than a particular child goes to the zoo. The number of children in her class is
(D) none of these
Sol. The number of times the teacher goes to the zoo = nC3
The number of times a particular child goes to the zoo = n-1C2
From the question , nC3 – n-1C2 = 84.
Or (n -1)(n –2)(n –3) = 6 × 84 = 9× 8 × 7
⇒ n – 1 = 9
⇒ n = 10
Hence (B) is the correct answer.