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Statistics Help

**Question: **(a) With the help of Venn diagrams, show that for finite sets A, B and C

|A ∪ B ∪ C| = |A| + |B| + |C| − |A ∩ B| − |B ∩ C| − |A ∩ C| + |A ∩ B ∩ C| .

(b) Each of the 63 first-year students studying computing at a university this year can

study a number of optional modules. If 16 choose to study the accounting option, 37

choose the business option and 5 study both of these options, how many students

take neither accounting nor business?

(c) Last year 25 students chose to study the accounting option, 27 chose the business

option and 12 chose the tourism option. There were 20 students who took both the

accounting and the business options, 5 who opted for accounting and tourism, and

3 who studied business and tourism. No students took all three options.

(i) How many students were taking at least one of the three options?

(ii) How many students were taking only tourism? Edit

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