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QUIZ 10: COUNTING 

(12 problems worth a total of 50 points) 

In a group of 110 students, 42 are taking Accounting, 38 are taking Business, and 48 are taking 

Communications. Of these, 11 are taking both accounting and business, 14 are taking both 

accounting and communications, 8 are taking both business and communications, and 3 are 

taking all three courses. 

1. Draw a Venn diagram to depict the problem and give the cardinalities of the disjoint sets. 

(6 points) 

2. How many students are taking at least one of accounting, business, or communications? 

(4 points) 

3. How many are not taking any of these three courses? (4 points) 4. How many are taking accounting and business, but not communications? (4 points) 

5. How many are taking business, but not accounting or communications? (4 points) 

6. How many are taking either accounting or business (or both), but not communications? 

(4 points) 

7. How many strings of length 5 over the set {a b c d e , , , , } are there if no element is repeated? 

(4 points) 

8. How many strings of length 5 over the set {a b c d e , , , , } are possible if letters can be repeated? 

(4 points) 

9. How many strings of length 3 over the set {a b c d e , , , , } are there if no element is repeated? 

(4 points) 

10. How many ways can the letters in the word STATISTICS be arranged? (4 points) 

11. How many subsets does a set of cardinality 11 have? (4 points) 

12. How many subsets of cardinality 7 does a set of cardinality 11 have? (4 points)

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