## mathmath333 one year ago 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?

1. 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}}

2. anonymous

if youre a mathtele why post this question, but the answer is 1

3. mathmath333

4. mathmath333

but the question is asking the number of weeks , how is this related to that ?

5. 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.

6. IrishBoy123

he is choosing 3 companions from 30, every week he visits the principal, so $C_{3}^{30}$

7. 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).

8. anonymous

So if it doesnt included himself would it be 29/3?