mathmath333
  • mathmath333
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?
Mathematics
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schrodinger
  • schrodinger
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mathmath333
  • mathmath333
\(\large \color{black}{\begin{align} & \normalsize \text{A class prefect goes to meet the principal every week.}\hspace{.33em}\\~\\ & \normalsize \text{His class has 30 people apart from him. If he has to take }\hspace{.33em}\\~\\ & \normalsize \text{groups of 3 every time he goes to the principal, in how }\hspace{.33em}\\~\\ & \normalsize \text{many weeks will he be able to go to the principal without }\hspace{.33em}\\~\\ & \normalsize \text{repeating the group of same 3 which accompanies him?}\hspace{.33em}\\~\\ & 1. \binom{30}{3} \hspace{.33em}\\~\\ & 2. \binom{29}{2} \hspace{.33em}\\~\\ & 3. \binom{29}{3} \hspace{.33em}\\~\\ & 4. \normalsize \text{none of these} \hspace{.33em}\\~\\ \end{align}}\)
anonymous
  • anonymous
if youre a mathtele why post this question, but the answer is 1
mathmath333
  • mathmath333
u mean answer is 1

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More answers

mathmath333
  • mathmath333
but the question is asking the number of weeks , how is this related to that ?
kropot72
  • kropot72
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.
IrishBoy123
  • IrishBoy123
he is choosing 3 companions from 30, every week he visits the principal, so \[C_{3}^{30}\]
mathmate
  • mathmate
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).
anonymous
  • anonymous
So if it doesnt included himself would it be 29/3?

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