Final answer:
By applying the principle of inclusion-exclusion, we find that all 20 students in the class play at least one game. Since the calculated number doesn't match any of the options provided, there may be a flaw or typo in the question.
Step-by-step explanation:
To determine how many students play one or both games, we can use the principle of inclusion-exclusion which is a fundamental principle in combinatorics. According to this principle:
- First, we add the total number of students playing each sport: 19 play football plus 10 play hockey.
- Next, we subtract the number of students that have been counted twice because they play both games: 6 play both.
Thus, the total number of students playing one or both games is (19 + 10 - 6).
Therefore, the calculation will be:
19 (football) + 10 (hockey) - 6 (both) = 23 students play one or both games.
However, since there are only 20 students in the class, it means that every student plays at least one game, and some play both. Hence, 20 students play one or both games.
But looking at the provided options (9, 10, 13, 15), none matches the calculated number. If we assume that the question might be wrongly structured or there is a typo, and it's asking for the number of students who play only one game, we can use the same principle:
23 (one or both) - 6 (both) = 17 students play only one game.
Again, the correct number is not in the options. Therefore, based on the provided information and options, the question may be flawed and might need clarification.