Final answer:
By using the principle of inclusion-exclusion, we find that 18 people out of a survey of 90 did neither tennis nor swimming.
Step-by-step explanation:
To determine how many people did neither activity in a survey of 90 people where 47 play tennis, 42 swim, and 17 do both, we use the principle of inclusion-exclusion. First, we add the number of people who play tennis and who swim:
47 (tennis) + 42 (swim) = 89.
We must then subtract the number of people who do both, since they have been counted twice:
89 - 17 (both) = 72.
This leaves us with the total number of people who do at least one activity. To find out how many did neither, we take the total number surveyed and subtract those who do at least one activity:
90 (total surveyed) - 72 (at least one activity) = 18.
Therefore, 18 people did neither activity.