Question

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?

Answer 1

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

Answer 2

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

Answer 3

u mean answer is 1

Answer 4

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

Answer 5

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.

Answer 6

he is choosing 3 companions from 30, every week he visits the principal, so

\[C_{3}^{30}\]

Answer 7

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).

Answer 8

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