Question

determine if the outcome of the event described would be found using a permutation or a combination. placing items in a line choosing cards from a deck of cards placing first or second in a rachoosing a committee of 5 people choosing 3 - digit lock combinations permutation combination

Explanation:

Step1: Recall the definition of permutation

Permutation is about arranging items where order matters.

Step2: Analyze each event

• Placing items in a line: Order of items in line matters (e.g., item A first vs item B first is different), so it's a permutation.
• Placing first or second in a race: Order (first - second) matters, so it's a permutation.
• Choosing 3 - digit lock combinations: The order of digits (e.g., 123 vs 321 is a different combination) matters, so it's a permutation.
• Choosing cards from a deck of cards: If we just choose cards (not arranging them in a sequence), order does not matter (e.g., choosing card A then card B is same as card B then card A when just considering the set of chosen cards), so it's a combination.
• Choosing a committee of 5 people: The group of 5 people (not their order within the group) is what matters, so it's a combination.

Answer:

Permutation: placing items in a line, placing first or second in a race, choosing 3 - digit lock combinations.
Combination: choosing cards from a deck of cards, choosing a committee of 5 people.