Question

decide if the situation involves permutations, combinations, or neither. explain your reasoning.

the number of ways 20 people can line up in a row for concert tickets.

does the situation involve permutations, combinations, or neither? choose the correct answer below.

a. neither. a line of people is neither an ordered arrangement of objects, nor a selection of objects from a group of objects.
b. combinations. the order of the 20 people in line does not matter.
c. permutations. the order of the 20 people in line matters.

Explanation:

Analyze the given scenario

Using the Permutations vs Combinations knowledge point

• The scenario asks for the number of ways 20 people can line up in a row.
• A line represents a sequential arrangement where each position (first, second, third, etc.) is distinct.
• Because changing the position of any two people in the line results in a different arrangement, the order of the people matters.

Determine the counting category

Using the Permutations vs Combinations knowledge point

• Since the order of arrangement is significant, this situation involves permutations.
• A permutation is an ordered arrangement of a set of objects.
• Therefore, the correct choice is C.

Answer:

• A. Neither. A line of people is neither an ordered arrangement of objects, nor a selection of objects from a group of objects.
• B. Combinations. The order of the 20 people in line does not matter.
• C. Permutations. The order of the 20 people in line matters. (Correct answer)