Question

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 equal to?

Answer 1

The number of children in her class is equal to :

Number of ways group of $3$ can be divided from $n$ number of students is equal to the number of times a teacher can go to the zoo $={}^{n}C_3$

Way of selecting $2$ students from $n-1={}^{(n-1)}C_2$

Therefore, as per given condition,

${}^{n}C_3–{}^{(n-1)}C_2=84$

On solving we get,

$n=10$

Hence the number of children in her class is equal to is $\mathit{n}\mathbf{}\mathbf{=}\mathbf{}\mathbf{10}$