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

Question

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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.

$\begin{array}{l} ^{n} C_{3} -^{n - 1} C_{2} = 84 \\ or (n - 1) (n - 2) (n - 3) = 6 \times 84 = 9 \times 8 \times 7 \\ \Rightarrow n - 1 = 9 \end{array}$

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

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