Exercise 8.12.20: Counting binary strings.
(a) How many binary strings of length 12 do not have exactly four 1's?
(b) How many binary strings of length 12 start with 101 or 1110?
(e) How many binary strings of length 12 start with 00 or end with 00 or both?
Exercise 8.12.20: Counting binary strings. (a) How many binary strings of length 12 do not have...
Problem 3 (Counting binary strings) 20 marks/ Consider all bit strings of length 15. 1. How many begin with 00? 2. How many begin with 00 and end with 11? 3. How many begin with 00 or end with 10? 4. How many have exactly ten 1's? 5. How many have exactly ten 1's such as none of these 1's are adjacent to each other? Provide detailed justifications for your answers. Problem 3 (Counting binary strings) 20 marks/ Consider all...
Multiple Choice How many strings of length 12 over the alphabet {a,b,c} have exactly three a's or have exactly three b's or have exactly three c's? (1?).22-3-(3) °(12):22-3-(?) (3) ° (13)-3-(1) QUESTION 20 Multiple Choice How many binary strings of length 12 have exactly six 1's or begin with a 0? ° (62) +211 -(0 ° (12) +201 - 1 ° (6) +211 -(5) ° (12) + 211
Consider all bit strings of length 12. How many have exactly four 1's?
Let A be the set of all bit strings of length 10. 1. How many bit strings of length 10 are there? How many bit strings of length 10 begin with 1101? How many bit strings of length 10 have exactly six 0's? How many bit strings of length 10 have equal numbers of O's and 1's? How many bit strings of length 10 have more O's than 1's? a. b. c. d. e.
consider all bit strings of length 12 How many have 8 0s and 4 1s that have exactly 3 consecutive 1s (allow 4 consecutive 1s)? A 90 В 72 С 45 D 36 E 9 consider all bit strings of length 12 How many have 8 0s and 4 1s that have exactly 3 consecutive 1s (allow 4 consecutive 1s)? A 90 В 72 С 45 D 36 E 9
PROJECT 2-COUNTING SUBSETS (BINARY STRINGS Choose 6 letters of the English alphabet including all the different characters in your family name (If you have more than & diffecent characters, choose the first 61. Let X be the set di all lower case vensions of the letters you have chosen. Let S be the set of all binary strings of length 6 (0 Using cofrect set notation, list the elements in set X. (u) ust all the subsets of X with...
Imprecise Counting - Long Runs in Binary Strings Let n=2^k for some positive integer k and consider the set Sn of all n-bit binary strings. Let c be an integer in {0,…,n−k}. Consider any j∈{1,…,n−k−c+1}. How many strings b1,…,bn∈Sn have bj,bj+1,…,bj+k+c−1=00…0? In other words, how many strings in Sn have k+c consecutive zeros beginning at position j? For each j∈{1,…,n−k+c+1}, let Xj be the subset of Sn consisting only of the strings counted in the previous question. Show that (n−k−c+1)∑(j=1)...
4. [6 marks] (Basic Counting) How many bit strings of length 10 contain either five consecutive 0s or five consecutive 1s?
Problem 3 a) How many strings are there of length 10 over the alphabet (a, b) with exactly five a's? b) How many strings are there of length 10 over the alphabet (a, b, c) with exactly five a's?
Help with Pascal’s Triangle: Paths and Binary Strings Suppose you want to create a path between each number on Pascal's Triangle. For this exercise, suppose the only moves allowed are to go down one row either to the left or to the right. We will code the path by using bit strings. In particular, a O will be used for each move downward to the left, and a 1 for each move downward to the right. So, for example, consider...