Question

answer the following question using arrangements with repetition, permutations, or combinations. be sure to explain why the particular counting technique applies to the problem.

the president must assign ambassadors to six different foreign embassies. from a pool of eleven candidates, how many different diplomatic teams can she form?

determine the appropriate counting technique. choose the correct answer below.

a. arrangements with repetition should be used because no item may be selected more than once and the order matters.
b. permutations should be used because no item may be selected more than once and the order matters.
c. permutations should be used because we make selections from a group of choices.
d. arrangements with repetition should be used because we make selections from a group of choices.
e. combinations should be used because no item may be selected more than once and the order does not matter.

Explanation:

Analyze the problem constraints

Using the Permutations, Combinations, and Arrangements with Repetitions knowledge points:

• We have a pool of 11 candidates.
• We must assign ambassadors to 6 different foreign embassies.
• Since each candidate can only be assigned to at most one embassy, no candidate (item) can be selected more than once (no repetition).
• Because the 6 embassies are distinct ("different foreign embassies"), assigning Candidate A to Embassy 1 and Candidate B to Embassy 2 is a different outcome from assigning Candidate B to Embassy 1 and Candidate A to Embassy 2. Thus, the order of selection matters.

Evaluate the options

Using the Permutations knowledge point:

• Since no item may be selected more than once and the order of selection matters, permutations must be used.
• Option B correctly states: "Permutations should be used because no item may be selected more than once and the order matters."

Answer:

• A. Arrangements with repetition should be used because no item may be selected more than once and the order matters.
• B. Permutations should be used because no item may be selected more than once and the order matters. (Correct answer)
• C. Permutations should be used because we make selections from a group of choices.
• D. Arrangements with repetition should be used because we make selections from a group of choices.
• E. Combinations should be used because no item may be selected more than once and the order does not matter.