Final answer:
Using the principle of inclusion-exclusion, it was determined that 500 people participated as only trainers in the workshop after calculating the overlap of those attending as both learners and trainers.
Step-by-step explanation:
Calculating the Number of Participants as Only Trainers
To determine how many people participated as only trainers in the workshop, we need to use the principle of inclusion-exclusion. The total number of people who attended the workshop is given as 2000. Out of these, 1500 participated as learners, and 800 participated as trainers. Some of these participants attended both as learners and trainers. To find the number exclusively attending as trainers, we subtract the total number of participants from the combined number of learner and trainer roles.
Add the number of learners and trainers: 1500 learners + 800 trainers = 2300.Since only 2000 people attended, the overlap of those who participated in both roles is 2300 - 2000 = 300.Subtract the overlap from the total number of trainers to get the exclusive trainers: 800 trainers - 300 = 500 trainers.
Therefore, 500 people participated as only trainers in the workshop.