Question

decide if the situation involves permutations, combinations, or neither. explain your reasoning.
the number of ways a five - member committee can be chosen from 14 people.
does the situation involve permutations, combinations, or neither? choose the correct answer below.
a. permutation. the order of the committee members matters.
b. combination. the order of the committee members does not matter.
c. neither. a line of people is neither an ordered arrangement of objects, nor a selection of objects from a group of objects.

Explanation:

To determine if it's a permutation, combination, or neither, we analyze the situation: choosing a five - member committee from 14 people. In a combination, the order of selection does not matter, while in a permutation, the order matters. For a committee, the order in which members are chosen does not matter (e.g., choosing person A then person B is the same as choosing person B then person A for the committee). So this is a combination situation. Option A is incorrect because order does not matter for a committee. Option C is incorrect as this is a selection of objects (people) from a group.

Answer:

B. Combination. The order of the committee members does not matter.