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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 the number of times she goes to the zoo is 84 more than a particular child goes to the zoo. Number of children in her class is

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answer is B.

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Detailed Solution

Let the number of students be

' n'

Number of children taken to zoo at a time = 3

Number of times the teacher goes to zoo $=^{n} C_{3}$

Each child goes to the zoo $=^{(n - 1)} C_{2}$ ways (leaving that child)

As per the problem,

$^{n} C_{3} = 84$

$\Rightarrow \frac{(n - 1) (n - 2) (n - 3)}{3 x 2 x 1} = 12 \times 7$

$\Rightarrow (n - 1) (n - 2) (n - 3) = 9 \times 8 \times 7$

$∴ n = 10$

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