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Posted: September 10th, 2021
Discrete Structures HW#5: Chapters 5 and 6 Assignment (Counting Techniques)
Complete the following questions very carefully. Upon completion and after checking and confirming your answers, go to blackboard and submit your answers in the multiple-choice section.
Q1. Write a word essay – Evaluate the Combination ?
Q2. Write a word essay – Evaluate the Combination ?
Q3. Write a word essay – Evaluate the Permutation ?
Q4. Write a word essay – Evaluate the Permutation ?
Q5. What is the number of permutations of a set of 6 elements?
Q6. A person wishes to purchase something from the Ice Cream Parlor that has seven different flavors of ice cream and ten different toppings. The person is going to get two scoops and a topping. How many different possible choices could they make?
Q7. The Martian calendar has sixteen months instead of twelve. What is the fewest number of Martians so that five of them will have the same birth-month?
Q8. Within a universal set of two hundred people, there are three subsets , and such that
, , ,
, , and .
How many people are in none of these sets?
Q9. Within a universal set of two hundred people, there are three subsets , and such that
, , ,
, , and .
How many people are in at least one of the sets?
Q10. A student wishes to take
an English Course (offered at 8, 10, 11 and 12),
a Math Course (offered at 9, 10, 12 and 1) and
a Comp Sci Course (offered at 9, 11, 12 and 1)
How many different schedules are possible so that they make take all three courses?
Q11. You are in a grocery store to purchase 10 pizzas, there are 5 varieties to choose from, in how many different ways you can purchase 10 pizzas providing a repetition is allowed?
Q12. Consider the equation W + X + Y + Z = 20, how many different solutions providing , we are only concerned with positive integers W, X, Y and Z.
Q13. Let S be a finite set containing 12 elements, which we wish to partition into Cells C1, C2, C3, and C4, such that n(C1) = 2, n(c2) = 2, n(C3) = 3, n(C4) = 5.
How many such partitions are possible?
Q14. List cycles’ sizes for the following permutation:
Q15. Suppose that you are looking at permutations of {1, 2, 3, 4, 5, 6, 7, 8}.
How many permutations are there with the cycle structure (a, b, c, d) (e, f, g, h)?
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