Question

1. of the 400 students surveyed, the number of students who participate in each club are shown in the venn diagram. which of the statements below is not justified by the information in the venn diagram?

a. there are 264 students who do not participate in the three clubs listed.
b. there are 15 students who participate in exactly two of the three clubs listed.
c. there are a total of 12 students in the craft club.
d. there are no students who participate in both craft club and flag football club but not board game club.

Explanation:

Step1: Analyze option a

The number of students who do not participate in any of the three clubs is \(400-(72 + 12+5 + 1+8+36)=400 - 134 = 266
eq264\), so option a is not justified by the Venn - diagram.

Step2: Analyze option b

The number of students who participate in exactly two of the clubs is \(5 + 8+1=14
eq15\), so option b is not justified by the Venn - diagram.

Step3: Analyze option c

The number of students in the Craft Club is \(12 + 5+1=18
eq12\), so option c is not justified by the Venn - diagram.

Step4: Analyze option d

From the Venn - diagram, we can see that there are no students in the part of the Flag Football Club that does not overlap with the Board Game Club, which means there are no students who participate in Flag Football Club but not Board Game Club.

Answer:

a. There are 264 students who do not participate in the three clubs.
b. There are 15 students who participate in exactly two of the three clubs listed.
c. There are a total of 12 students in the Craft Club.
d. There are no students who participate in both Craft Club and Flag Football Club but not Board Game Club.