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.

calculate how many different diplomatic teams are possible.
(type a whole number.)

Explanation:

Analyze the counting scenario

Using the Permutations and Combinations knowledge points

• We must assign 11 candidates to 6 distinct foreign embassies.
• Each candidate can be assigned to at most one embassy (no item selected more than once).
• The embassies are different, so assigning candidate A to embassy 1 and candidate B to embassy 2 is different from assigning B to embassy 1 and A to embassy 2 (order matters).

Determine the appropriate counting technique

Using the Permutations knowledge point

• Since order matters and repetition is not allowed, permutations must be used.
• This matches option B: "Permutations should be used because no item may be selected more than once and the order matters."

Calculate the number of diplomatic teams

Using the Permutations knowledge point

$$ P(11, 6) = \frac{11!}{(11-6)!} = \frac{11!}{5!} $$

$$ P(11, 6) = 11 \times 10 \times 9 \times 8 \times 7 \times 6 = 332,640 $$

Answer:

Question 1

• (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.

Question 2

The number of different diplomatic teams is <blank>332640</blank>.