A class prefect goes to meet the principal every week. His class has 30 people apart from him. If he has to take groups of 3 every time he goes to the principal, in how many weeks will he be able to go to the principal without repeating the group of same 3 which accompanies him?

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A class prefect goes to meet the principal every week. His class has 30 people apart from him. If he has to take groups of 3 every time he goes to the principal, in how many weeks will he be able to go to the principal without repeating the group of same 3 which accompanies him?

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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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\(\large \color{black}{\begin{align} & \normalsize \text{A class prefect goes to meet the principal every week.}\hspace{.33em}\\~\\ & \normalsize \text{His class has 30 people apart from him. If he has to take }\hspace{.33em}\\~\\ & \normalsize \text{groups of 3 every time he goes to the principal, in how }\hspace{.33em}\\~\\ & \normalsize \text{many weeks will he be able to go to the principal without }\hspace{.33em}\\~\\ & \normalsize \text{repeating the group of same 3 which accompanies him?}\hspace{.33em}\\~\\ & 1. \binom{30}{3} \hspace{.33em}\\~\\ & 2. \binom{29}{2} \hspace{.33em}\\~\\ & 3. \binom{29}{3} \hspace{.33em}\\~\\ & 4. \normalsize \text{none of these} \hspace{.33em}\\~\\ \end{align}}\)
if youre a mathtele why post this question, but the answer is 1
u mean answer is 1

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Other answers:

but the question is asking the number of weeks , how is this related to that ?
Say the prefect chooses group A to accompany him on the first week. On the second week he only needs to ensure he does not pick all the same students as in group A.
he is choosing 3 companions from 30, every week he visits the principal, so \[C_{3}^{30}\]
It is much less confusing to give the answer instead of the shorthand. @mitchal means choice #1, \(\left(\begin{matrix}30 \\ 3\end{matrix}\right)\) weeks because order does not count, and we need to find the number of distinct groups of three students, not including himself (31st student in the class).
So if it doesnt included himself would it be 29/3?

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