How many strings of length 9 over the alphabet {a, b, c} are there which contain at least seven consecutive a’s? Hint: Upon writing down a few such strings you will notice that they must take one of three distinct forms (depending on where the consecutive a’s are). Then use the inclusion–exclusion principle.

How many strings of length 9 over the alphabet {a, b, c} are there which contain at least seven consecutive a’s? Hint: Upon writing down a few such strings you will notice that they must take one of three distinct forms (depending on where the consecutive a’s are). Then use the inclusion–exclusion principle.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Related questions

Q: How many distinct ten-digit passwords are possible if you must use at least one 26 lower case letter…

A: Given: you must use at least one 26 lower case letter from {a, b, . . . , z}, at least one 26 upper…

Q: string has at least one 1 and at least one 0. (c) The string contains exactly five 1's or it…

A: The string has at least one 1 and at least one 0. This removes the possibility of all one and all…

Q: Combinatorial questions: A bit have 2 states: 0 and 1. If bit could have 4 states (0, 1, 2, 3), how…

A: ans (d) and (e)

Q: How many strings of six uppercase letters are there that contain at least one ' or at least one 'Q'…

Q: How many strings of letters from the set (A, B} have length 11 and have exactly 4 A's (repeated…

A: The Answer is given in step-2.

Q: A. Compute the total number of sets (of size 5) containing exactly 2 elements from X and 3 elements…

Q: Use inclusion-exclusion to find the number of ways to arrange the six numbers 1, 2, 3, 4, 5, 6 such…

A: please see the next step for solution

Q: Please give me the definition of the R codes below. What does it use for and indicate?…

A: Given some R codes. We have to define these R codes.

Q: How many different strings can be made from the letters in ATTRACTION, using all the letters, if all…

A: The given word is ATTRACTION

Q: Consider strings of length n, n ≥ 1, over the set (a, b, c, d). (a) How many such strings contain at…

A: (a)Total strings that contain at least one pair of adjacent characters that are the same = Total…

Q: There are 25 books arranged on a shelf. Answer the following questions with justification. Describe…

Q: ). Let X be the set of the 26 lowercase English letters and 10 decimal digits. How any X-strings of…

A: The first symbol can be chosen in 10_C_{1} = 10 ways.The last symbol can be chosen in 9_c_{1} = 9…

Q: Combinatorial questions: A bit have 2 states: 0 and 1. If bit could have 4 states (0, 1, 2, 3), how…

A: Hi! Thank you for the question, As per the honor code, we are allowed to answer three sub-parts at a…

Q: The lower boundary of modal class with size 15 is 40.The frequency of this class is 7. Find the mode…

A: Size of class is 15, and lower boundary is 40.

Q: Determine the number of strings of length 10 from the alphabet {A, B, C} that contain exactly 3 A's…

Q: a set blocks contain blocks of height 1, 2, 4 centimeters. Towers can be contructed by piling some…

Q: For any integer n ≥ 4, determine the number of hexadecimal strings of length n in which the digit A…

A: In hexadecimal system, there are 16 possible letters or digits. [ 0 - 9, A - F ]

Q: How many bit strings of length 10 has at least 4 1s? Select one: O a. 210 O b. O C. O d. IME IMA i=0…

Q: How many 5-bit strings contain the string "100" as a consecutive substring? Define the following…

A: Note: We shall only answer up to first three sub-parts. GIven, Hence, according to given conditions…

Q: A password is a string of length 5, each character of which is from the set (x,y,z) of letters.How…

A: There are 3 letters and the password is a string of length 5 characters. When the password uses all…

Q: Consider strings of length n, n 2 1, over the set (a, b, c, d}. (a) How many such strings contain at…

A: Given - Consider strings of length n, n ≥ 1, over the set a, b, c, d To find - How many such…

Q: If 1/3 of the blocks in set A are red, and 1/4 of the blocks in set B are red, does it follow that…

A: Given 1/3 of blocks in set A are red and 1/4 of blocks in set B are red

Q: A pizza restaurant sells pizzas in three sizes, and a customer can choose up to three toppings,…

A: The objective of this question is to find out the total number of pizza configurations possible…

Q: Suppose that you had infinitely many people, each one wearing a uniquely numbered button: 1, 2, 3,…

A: Infinitely many people and each wearing uniquely numbered butten(1,2,3.....) Now everyone flipping…

Q: How many strings of length 10 over the alphabet {a, b, c, d} have exactly 3 a's? O () O 47 O () - 37…

Question

How many strings of length 9 over the alphabet {a, b, c} are there which contain at least seven consecutive a’s?

Hint: Upon writing down a few such strings you will notice that they must take one of three distinct forms (depending on where the consecutive a’s are). Then use the inclusion–exclusion principle.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1: Finding the Sets

VIEW

Step 2: Applying the Inclusion-Exclusion Principle

VIEW

Solution

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps

SEE SOLUTION Check out a sample Q&A here

Similar questions

Q5
Help me fast with detail explanation. Definitely I will give Upvote.
et S be the set of all strings of 0's and 1's of length 4, and let A and B be the following subsets of S. A = {1001, 1000, 1010, 0110} and B = {0101, 1101, 0110, 1110} nd each of the following. (Enter your answers in set-roster notation.) a) AnB = (b) AUB = (c) A - B = (d) B - A =
4. Consider the set of all strings of a's, b's, c's and d's. (a) Make a list of all of these strings of length zero, one, and two that do not contain the pattern bb. (b) For each integer n > 0, let sn = the number of strings of a's, b's, c's and d's of length n that do not contain the pattern bb. Find so, s1, and s2. (c) Find a recurrence relation for the sequence s0, S1, S2, . ..
Let S be the set of all bit strings (strings of 0's and I's) Select one: O A. f(s) = the string obtained by moving the first bit of s to the end of the string. (For example, f(1001101) = 0011011) O B. f(s) = the string obtained from s by interchanging 0's and I's. (For example, f(11000) = 00111) O c. f(s) the string & with a 1 bit appended at the end. (For example, f(1101) = 11011) O D. f(s) the reversal of s. (For example, f(110) = 011) length at least 2. Which of the following functions f : S → S is not onto S?
Show that S has 2n subsets.
How many distinct selections of 4 objects are possible from the multiset {2·a,3·b,4·c,5·d}, assuming that we don’t make distinctions based on ordering once a selection is made? (i.e., 2 a’s and 2 b’s will count once, as opposed to separately for, e.g., aabb vs. abab)
Let S be the set of all strings of 0's and 1's of length 4, and let A and B be the following subsets of S. A = {0111, 1011, 0100, 0110} and B = {0010, 1010, 0111, 1110} Find each of the following. (Enter your answers in set-roster notation.) (a) AnB = (b) AUB= (c) A - B = (d) B-A = X X
A user is allowed to create an 8-digit password, but it must satisfy the following requirements: The first 2 spots must be different letters of the alphabet (case is not sensitive) The next 4 spots must be different numbers from the set {0-9} The last 2 spots must be different non-alphanumeric symbols from the set {# , @, $,%} How many passwords are possible?