How many strings of 10 decimal digits are there that contain the following combinations of number...
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
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How many strings of 10 decimal digits are there that contain the following combinations of number...
How many strings of four decimal digits (Note there are 10 possible digits and a string can be of the form 0014 etc
How many strings of four decimal digits (Note there are 10 possible digits and a string can be of the form 0014 etc., i.e., can start with zeros.) (a) have exactly three digits which are 9s?
Let A be the set of all bit strings of length 10. 1. How many bit...
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.
1. (a) (i) How many different six-digit natural numbers may be formed from the digits 2,...
1. (a) (i) How many different six-digit natural numbers may be formed from the digits 2, 3, 4, 5, 7 and 9 if digits may not be repeated? (ii) How many of the numbers so formed are even? (iii) How many of the numbers formed are divisible by 3? (iv) How many of the numbers formed are less than 700,000? (b) JACK MURPHY’s seven character password consists of four let- ters chosen from the ten letters in his name (all...
1. Find expressions for each of the following. (Leave your answer as a mathematical expression rather than a number.) (a) The number of strings of 8 lower case letters (a-z) that do not contain any l...
1. Find expressions for each of the following. (Leave your answer as a mathematical expression rather than a number.) (a) The number of strings of 8 lower case letters (a-z) that do not contain any letter more than once. (b) The number of binary strings of length 10 that contain at most two Os. (c) The number of subsets of 11,2,,10 with three elements that contain at least one even number and at least one odd number. [Give brief justifications.]...
Question 5# (Combinations, including stars and bars') Problem: How many PINs have digit suam 20? (A PIN is string abcd of 4 decimal digits eg 6806) As a first attempt at answering this: (a) H...
Question 5# (Combinations, including stars and bars') Problem: How many PINs have digit suam 20? (A PIN is string abcd of 4 decimal digits eg 6806) As a first attempt at answering this: (a) How many different solutions in non-negative integers has the equation a+b+c+d-20? Hint: 20 stars and 3 bars. The count in (a) is much too big for our problem because it includes many solutions that contain non-decimal digits; ie. values of a, b, c or d that...
Question 1 (a) How many positive integers are there between 1000 and 4999, inclusive? (b) How...
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...
1.How many possible orderings of letters ABCDEFG are there? 2.How many strings of length 4 can be made using the letters...
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...
, In a standard set of double-six dominoes, there is exactly one domino for every possible...
, In a standard set of double-six dominoes, there is exactly one domino for every possible (unordered) pair of numbers from 0 to 6 (including doubles, i.e. a domino with two fives.) A "hand" of dominoes is another word for a set of dominoes. (a) How many dominoes are there (show your work)? (b) How many five-domino hands are there? (c) How many five-domino hands contain no domino with a 0? (d) How many five-domino hands contain at least one...
Find how many positive integers with exactly four decimal digits, that is, positive integers between 1000 and 9999 inclusive, have the following properties: (a) are divisible by 5 and by 7
Find how many positive integers with exactly four decimal digits, that is, positive integers between 1000 and 9999 inclusive, have the following properties: (a) are divisible by 5 and by 7. (b) have distinct digits. (c) are not divisible by either 5 or 7.
If the number is a decimal please include 4 digits past the decimal point if available....
If the number is a decimal
please include 4 digits past the decimal point if available.
3 0/2 points Previous Answers PSE6 4.P.011 My Notes In a local bar, a customer slides an empty beer mug down the counter for a refill. The bartender is momentarily distracted and does not see the mug, which slides off the counter and strikes the floor 0.40 m from the base of the counter. The height of the counter is 0.820 m. (a) With...
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.
1. Find expressions for each of the following. (Leave your answer as a mathematical expression rather than a number.) (a) The number of strings of 8 lower case letters (a-z) that do not contain any letter more than once. (b) The number of binary strings of length 10 that contain at most two Os. (c) The number of subsets of 11,2,,10 with three elements that contain at least one even number and at least one odd number. [Give brief justifications.]...
Question 5# (Combinations, including stars and bars') Problem: How many PINs have digit suam 20? (A PIN is string abcd of 4 decimal digits eg 6806) As a first attempt at answering this: (a) How many different solutions in non-negative integers has the equation a+b+c+d-20? Hint: 20 stars and 3 bars. The count in (a) is much too big for our problem because it includes many solutions that contain non-decimal digits; ie. values of a, b, c or d that...
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...
, In a standard set of double-six dominoes, there is exactly one domino for every possible (unordered) pair of numbers from 0 to 6 (including doubles, i.e. a domino with two fives.) A "hand" of dominoes is another word for a set of dominoes. (a) How many dominoes are there (show your work)? (b) How many five-domino hands are there? (c) How many five-domino hands contain no domino with a 0? (d) How many five-domino hands contain at least one...
If the number is a decimal
please include 4 digits past the decimal point if available.
3 0/2 points Previous Answers PSE6 4.P.011 My Notes In a local bar, a customer slides an empty beer mug down the counter for a refill. The bartender is momentarily distracted and does not see the mug, which slides off the counter and strikes the floor 0.40 m from the base of the counter. The height of the counter is 0.820 m. (a) With...
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