Using the set S = {1,2,3},
(1) how many choices have a length of 10 and contain five 1's?
(2) how many choices have a length of 10 and contain at least one 3?
Using the set S = {1,2,3}, (1) how many choices have a length of 10 and...
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.
How many 4-digit numbers can be formed using only the digits {1,2,3} if repetition is allowed and the number must contain the digit 3 somewhere. Hint: it may be easier to first count the numbers that don't contain the digit 3.
Express as a set using set-builder notation The set of all binary strings that contain at least one 0 and at least one 1. The set of all binary strings with even length. The set of all binary strings that contain an even number of 1’s. The set of all binary strings that read the same forward and backwards
Let the universal set S be S = {1,2,...,10}, and A = {1,2,3}, B = {3,4,5,6,7} and C = {7,8,9,10} 1) Find (A∪C)−B 2) Find A^c ∩(B^c ∪C)
1.How many possible orderings of letters ABCDEFG are there? 2.How many strings of length 4 can be made using the letters ABCDEFG? 3.How many subsets of size 4 are there of the letters ABCDEFG. 4.How many possible strings are there of the letters "MATTER"? 5.Consider four books: an engineering book (E), a physics book (P), a history book (H), and an Art book (A). Consider the following problem: Suppose that the library has at least six copies of each of...
Question 1 (a) How many positive integers are there between 1000 and 4999, inclusive? (b) How many positive integers between 1000 and 4999, inclusive: 1. have no repeated digit? 2. have at least one repeated digit? 3. have at most two repeated digits? Note that by 'one repeated digit' we mean that there is a digit that appears at least twice (eg, 1123 has one repeated digit). Similarly, by two repeated digits we mean a digit that appears at least...
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?
This is discrete mathematics. 1. 5 points] Let T be the set of strings whose alphabet is 10, 1,2,3) such that, in every element of T a. Every 1 is followed immediately by exactly one 0. b. Every 2 is followed immediately by exactly two 0s. c. Every 3 is followed immediately by exactly three 0s. For instance, 00103000 E T.) Find a recursive definition for T 1. 5 points] Let T be the set of strings whose alphabet is...
How many strings of 10 decimal digits are there that contain the following combinations of numbers? Show your work. You may leave your answer in terms of an expression involving factorials/exponents. One 0, four 2’s, and five 8’s Exactly one 1, two 3’s, and one 7 (the other six digits can be anything