Question

six sales representatives for a company are to be chosen at random to participate in a training program. the company has eighteen sales representatives, three in each of six regions. what is the probability that the six sales representatives chosen to participate in the training program will be from only two of the six regions?

the probability is \square.
(round to four decimal places as needed.)

Explanation:

Calculate total outcomes

Using the Combinatorics knowledge point

$$ N = \binom{18}{6} = \frac{18 \times 17 \times 16 \times 15 \times 14 \times 13}{6 \times 5 \times 4 \times 3 \times 2 \times 1} = 18564 $$

Select two regions

Using the Combinatorics knowledge point

$$ N_{\text{regions}} = \binom{6}{2} = 15 $$

Choose representatives from selected regions

Using the Combinatorics knowledge point

$$ N_{\text{reps}} = \binom{3}{3} \times \binom{3}{3} = 1 \times 1 = 1 $$

Calculate favorable outcomes

Using the Combinatorics knowledge point

$$ N_{\text{favorable}} = N_{\text{regions}} \times N_{\text{reps}} = 15 \times 1 = 15 $$

Calculate final probability

Using the Classical Probability knowledge point

$$ P = \frac{15}{18564} \approx 0.000808016 \approx 0.0008 $$

Answer:

Six sales representatives for a company are to be chosen at random to participate in a training program. The company has eighteen sales representatives, three in each of six regions. What is the probability that the six sales representatives chosen to participate in the training program will be from only two of the six regions?

The probability is <blank>0.0008</blank>.
(Round to four decimal places as needed.)