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Select the correct answer from each drop-down menu.

Determine whether each situation describes a permutation or a combination.

| Situation | Permutation or Combination? |
|--------------------------------------------------------------------------|-----------------------------|
| The Junior class elects 3 representatives to the student council. | |
| The swim team must choose a captain and co-captain. | |
| A sandwich made with 3 of the 25 available toppings. | |
| A locker has a 5-digit code that must be entered to open it. | |

Sagot :

GinnyAnsweridn
Let's analyze each situation to determine whether it describes a permutation or a combination:

### Situation 1
The Junior class elects 3 representatives to the student council.

In this situation, the order in which the representatives are chosen does not matter. We are only interested in choosing a group of 3 representatives out of the whole class. This is an example of a combination.

### Situation 2
The swim team must choose a captain and co-captain.

Here, the order of selection matters because the role of captain is different from the role of co-captain. This means we need to consider the different possible ways to assign these roles. This is an example of a permutation.

### Situation 3
A sandwich made with 3 of the 25 available toppings.

For the sandwich, the order in which the 3 toppings are chosen does not matter. We only care about which 3 toppings are selected out of the 25 available. This is an example of a combination.

### Situation 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 because the code must be entered in a specific sequence to unlock the locker. This means we need to consider the different possible sequences of the 5 digits. This is an example of a permutation.

### Summary
1. The Junior class elects 3 representatives to the student council: Combination
2. The swim team must choose a captain and co-captain: Permutation
3. A sandwich made with 3 of the 25 available toppings: Combination
4. A locker has a 5-digit code that must be entered to open it: Permutation

Now filling these into the table:

\begin{tabular}{|l|l|}
\hline \multicolumn{1}{|c|}{ Situation } & \begin{tabular}{c}
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{tabular}