Let's determine whether each of the given situations is a permutation or a combination.
1. The Junior class elects 3 representatives to the student council.
- In this scenario, the order in which the representatives are selected does not matter. We are simply choosing 3 out of many students. Hence, this is a Combination.
2. The swim team must choose a captain and a co-captain.
- Here, the order is important because the roles are different (captain and co-captain). Choosing A as captain and B as co-captain is different from choosing B as captain and A as co-captain. Hence, this is a Permutation.
3. A sandwich made with 3 of the 25 available toppings.
- In this case, the order in which the toppings are chosen does not affect the result, as any combination of 3 toppings will make the same sandwich regardless of order. Hence, this is a Combination.
4. A locker has a 5-digit code that must be entered to open it.
- For the locker code, the order of the digits is crucial for opening the locker. A code of 12345 is different from 54321, for example. Hence, this is a Permutation.
Putting it all together:
[tex]\[
\begin{array}{|l|l|}
\hline \multicolumn{1}{|c|}{ Situation } & \begin{tabular}{l}
Permutation or \\
Combination?
\end{tabular} \\
\hline \begin{tabular}{l}
The Junior class elects 3 representatives to \\
the student council.
\end{tabular} & Combination \\
\hline \begin{tabular}{l}
The swim team must choose a captain and \\
co-captain.
\end{tabular} & Permutation \\
\hline \begin{tabular}{l}
A sandwich made with 3 of the 25 available \\
toppings.
\end{tabular} & Combination \\
\hline \begin{tabular}{l}
A locker has a 5-digit code that must be \\
entered to open it.
\end{tabular} & Permutation \\
\hline
\end{array}
\][/tex]
