Question

A teacher takes three children from her class to the zoo at a time as often as she can, but she doesn’t take the same set of three children more than once. She finds out that she goes to the zoo 84 times more than a particular child goes to the zoo. Total number of students in her class is equal to 

(A)  12 

(B)  14 

(C)  10 

(D)  11 

Answer 1

Correct option  (C) 10 

Let the number of students be n. Then total number of times the teacher goes to zoo is equal to ⁿC₃ and total number of times, a particular student goes to the zoo is equal to ^n-1C₂ . Thus