Question

select the correct answer from each drop-down menu.
determine whether each situation describes a permutation or a combination.

situation	permutation or combination?
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.

Explanation:

Step1: Recall Permutation vs Combination

Permutation: Order matters (e.g., choosing positions with distinct roles).
Combination: Order does not matter (e.g., choosing a group where roles are identical).

Step2: Analyze Each Situation

1. Electing 3 representatives:

The representatives have the same role (no order matters). So, this is a Combination.

1. Choosing captain and co - captain:

Captain and co - captain are distinct roles (order matters: person A as captain vs person A as co - captain is different). So, this is a Permutation.

1. 3 toppings from 25:

The order of putting toppings on a sandwich does not matter (a sandwich with lettuce, tomato, onion is the same as onion, tomato, lettuce). So, this is a Combination.

1. 5 - digit locker code:

The order of digits in the code matters (e.g., 12345 is different from 54321). So, this is a Permutation.

Answer:

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