Final answer:
The probability that all six chosen sales representatives come from the same region when selecting from 15 representatives across five regions depends on the assumption that there is an equal distribution. It involves calculating the conditional probability of each subsequent choice after the first, resulting in a product of probabilities.
Step-by-step explanation:
The question asks about the probability that all six chosen sales representatives come from the same region when selecting from a group of 15 representatives that are distributed across five regions. To calculate this, we must consider that the selection is done without replacement, and presume that the regions are evenly represented. Supposing each region has an equal number of representatives, there would be 3 representatives per region (15 total representatives/5 regions = 3 representatives per region).
When we select the first representative, it doesn't matter which region they come from, but each subsequent selection must be from the same region to meet the criteria. Therefore, the probability for each subsequent choice after the first (assuming an even distribution) would be:
2nd rep: 2/14 (since there are now only two reps left in the chosen region out of the remaining 14),
3rd rep: 1/13,
4th rep: 2/12 (since one rep from the other group might have been taken, we still have two left in the chosen region),
5th rep: 1/11,
6th rep: 2/10.
Multiply these probabilities together to get the chance that all six reps are from the same region:
(1/1) * (2/14) * (1/13) * (2/12) * (1/11) * (2/10).
Note: This is a simplified example presuming an equal distribution, and actual conditions may change the calculation.