cs离散结构代写 CS 2100代写 Discrete Structures代写

CS 2100: Discrete Structures

Homework 5

cs离散结构代写 1. Exercise 19 on page 384. These questions have the same answer. (i) How many eight-digit binary sequences have three 1’s, no two of which are

1. Exercise 19 on page 384.

These questions have the same answer.

(i) How many eight-digit binary sequences have three 1’s, no two of which are adjacent?

(ii) How many three elements subsets of {1, 2, 3, 4, 5, 6} are there?

Here is a function that demonstrates this fact: Given an eight-digit binary sequence containing three 1’s, no two of which are adjacent, write down the three positions containing the 1’s.

Decrease the second number you wrote by 1, and decrease the third number by 2.

(a) Describe in words the reverse function.

(b) Fill in the table below to illustrate the correspondence.

10101000	{1, 2, 3}
01010100
00010101
	{1, 3, 5}
	{1, 3, 6}
	{3, 4, 5}
	{2, 4, 6}

2. cs离散结构代写

Charlie and her girlfriend, Amber, go to lunch at a restaurant with 7 sandwiches on the menu.

There are also 5 beverages on the menu. How many possible two-sandwich, two-drink meals can they order (regardless of which of them orders first)…

a) if they order different sandwiches and drinks from each other?

b) if they each order without concern for what the other ordered?

3.

A small civil rights non-profit is selecting 3 of its 15 employees to form a task force focused on voting rights.

a) How many such task forces could they possibly select?

b) How many possibilities are there if they assign each member of the task force a unique role?

4. cs离散结构代写

A student club focused on diversity is forming a recruitment committee consisting of 7 of its 30 members. Out of 30 members total, 10 of the club’s members identify as gay and 5 identify as asexual. How many ways are there to form a recruitment committee which includes at least 3 members from each of these groups (meaning at least 3 gay and at least 3 asexual students)?

5. Exercise 21 on page 396. cs离散结构代写

The professor in your class asks each of the 30 students in the class his or her birthday, writing their responses as an ordered list of length 30. Assume no one of born on February 29.

(a) How many different results are possible?

(b) Of these, for how many are there no duplicate birthdays listed?

(c) What percent of the possible results have a duplicate birthday? Is this percent higher than you expected, lower than you expected, or about what you expected?

6. Exercises 24.a and 32 on pages 396-397. cs离散结构代写

A certain club is forming a recruitment committee and the club has two members named Jack and Jill. They have calculated that 2,380 of committees have Jack on them, 2,380 have Jill, 1,820 have Jack but not Jill, 1,820 have Jill but not Jack, and 560 have both Jack and Jill.

(a) How many committees have either Jack or Jill?

(b) Here is an algorithm for the problem above: “There are 2,380 committees that have Jack, and 2,380 that have Jill. By the sum rule, there are 2,380 + 2,380 = 4,760 that have either Jack or Jill.” Explain the error, and correct the algorithm.

7. Exercise 18 on page 407. cs离散结构代写

Suppose a shipment of 100 computers contains four defective computers, and we choose a sample of six computers.

(a) How many different samples are there?

(b) Of these, how many samples contain all four defective computers? What percent of the total does this represent?

(c) How many samples contain one or more defective computers? What percentage of the total does this represent?

8. cs离散结构代写

You conduct an experiment in which you interview a large number of families, each of which has 5 children. For each family, you write down the biological sex (M for male, F for female, I for intersex) of the children, in order from oldest to youngest.

a) How many possible results are there?

b) Out of all the possible results, how many have exactly two I’s?

c) Out of all the possible results, how many have at least one I, one F, and two M’s?

9. cs离散结构代写

A group of students is surveyed about race and gender identity for research purposes. The survey lists 6 categories for race and 4 categories for gender. Determine how many different survey results are possible, given each of the following constraints:

a) Students are allowed to check exactly 1 box under race and 1 box under gender.

b) Students are allowed to check 1 or 2 boxes under race and 1 or 2 under gender.

c) Students are allowed to check as many boxes as they wish (including 0).

10. Exercise 4 on page 417. cs离散结构代写

You are tracking your favorite baseball player by writing down his performance in 10 successive plate appearances using an ordered list of length 10.

(a) If you use H for a hit, S for a strikeout, B for a base-on-ball, and O for anything else, how many results are possible.

(b) Of the total, how many have exactly three H’s?

(c) Of the total, how many have exactly four H’s, exactly one S, exactly two B’s, and exactly three O’s.

11. Exercise 22 on page 418. cs离散结构代写

How many different bags of produce can I bring back from the store, assuming that there are apples, bananas, oranges, and peaches available; I buy at least one of each; and I purchase exactly 15 pieces of fruit altogether?

12. Consider the set of letters, tL, G, B, T, Q, I, Au:

a) How many ways are there to form a string containing exactly one copy of each letter?

b) Suppose all license plates in a certain state consist of three distinct consonants followed by two distinct vowels. How many such license plates can be formed from the given set?

c) Suppose three letters are chosen from this set at random (repeats allowed); what are the odds that at least one of them is a vowel (rounded to four digits)?

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