Answer:
63 people
Step-by-step explanation:
We have the following:
Let P: the subset of those 25 who would not go to a park
Let B: the subset of those 27 who would not go to the beach
Let C: the subset of those 24 that would not go to a cottage
Thus:
The intersection PB of subsets P and B consists of 10 people (i.e. neither a park nor a beach)
The intersection BC of subsets B and C consists of 7 people (i.e. neither beach nor cottage)
The intersection PC of subsets P and C consists of 6 people (i.e. neither a park nor a cottage)
We are also told that the PBC intersection of subsets P, B, and C consists of 4 person (i.e. would not go to a park, beach, or cottage)
The complement of the union of the sets P, B and C for the whole group consists of 6 people (that is, willing to go to the three places)
The formula to apply is as follows:
# (PUBUC) = #A + #B + #C - #AnB - #BnC - #AnC + #AnBnC
Replacing:
= 25 + 27 + 24 - 10 - 7 - 6 + 4
= 57 people
those who are willing to all who are 6 would be missing us, therefore:
57 + 6 = 63
The group consists of a total of 63 people.
