Discrete Mathematics How many n-digit numbers are there with at least one of the digits 1 or 2 or 3 absent (leading zeros are OK)?

Q: the set {1,3,4,6,7,8,9}, how many odd numbers can we construct between 100-999 if each element can…

A: We have to solve given problem:

Q: Prove by mathematical induction that the sum of cubes of three consequtive positive integers n is…

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Q: 0. How many handshakes are performed if all 100 senators shake each of the other senator's hand? Is…

A: We are going to use the following observations.

Q: Telephone area codes are three-digit numbers. The first digit is not 0 nor 1. How many three-digit…

A: The number of digits in Telephone are 3.

Q: determine whetherthe statement is true or false. If it is false, explain why or givean example that…

A: A statement is true for all natural numbers if for each natural number the statement holds true. One…

Q: 5. How many integers from 1000 through 9999 must you pick in order to be sure that at least two of…

A: Considering the integers from 1000 to 9999, which are all 4-digit integers. There are 10 possible…

Q: A-(kikis a positive integer and 22 <k< 30). 22, n(A)-B

A: Given that, the set A=k|k is a positive integer and 22&lt;k&lt;30  Obtain the elements in the set A.…

Q: 92. How many three-digit numbers, each less than 500, can be formed from the digits 1, 3, 4, 6, and…

A: Given digits is1,3,4,6,7 3 ways to fill it  (i.e 1,3, or 4) 4 ways to fill it 3 ways to fill it…

Q: The natural numbers are N= {1,2,3,...}. The prime numbers are P = {2,3,5,7..}. True or false? 74 P…

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Q: How many 3-digit numbers can be forms from the four digits 0,1,2,3 if: a) no two digits are to be…

A: 1) a) No two digits are to be the same, that is there is no repetation. Do remember, we are making…

Q: 5. s* -1 is a multiple of 8 for all natural numbers n

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Q: password for a website consists of 4 digits followed by 2 lowercase letters. Determine how many…

A: The total number of digits is 10. That is, {0,1,2,3,4,5,6,7,8,9}. The lower case letters are 26.…

Q: How many possible 6 digit numbers are there where all of the digits are different? Remember that a…

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Q: 12. How many positive integers less than 1000 are divisible by either 13 or 17? a) 134 b) 130 c) 76…

A: First check the divisibility for 13 then 17 then common in both.

Q: Three - digit numbers are formed from the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. a.) How many…

A: Solution

Q: how many positive month numbers are between 50 and 100: a. the one that was divisible by 7? which…

A: Solution a) Total numbers divisible by 7 between 1 to 100 are 1007=14 and total numbers divisible by…

Q: How many permutations of the letters PRODUCT have consonants in the second and third positions?

A: There are total 400 permutations of the letters PRODUCT have consonants in the second and third…

Q: 10. How many numbers between 11 and 200 are exactly divisible by 7? Find their sum.

A: To Find : a) number of integers between 11 and 200 that are exactly divisible by 7. b) Sum of…

Q: Counting numbers are to be formed using only the digits 2, 1, 4, 8, 9, 6, and 3. Determine the…

A: The objective is to determine the number of different possibilities for​ two-digit numbers which are…

Q: Statistics and probability: How many odd 3-digit positive integers greater than 20 are there?

A: We write a code to solve the task using python in Jupyter notebook.

Q: Bob is a stamp collector. His collection consists of three books. Two-tenths of his stamps are in…

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Q: et S be the set of positive integers less than 500. Find the number of integers in S that are…

A: Given query is to find the number of integers.

Q: Counting numbers are to be formed using only the digits 9,4,8,1 and 2. Determine the number of…

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Q: How many numbers from 1 to 1000 are not divisible by 2, 3 or 5?

A: We will count how many numbers are multiples of at least one of these three 2, 3 and 5 and then…

Q: 5. Use deductive reasoning to show that the following procedure always produces the number 5.…

A: Given procedure is :Pick a number. Add 4 to the number and multiply the sum by 3. Substract 7 and…

Q: 3. Two-digit numbers are formed, with replacement, from the digits 0-9. a. How many two-digit…

A: Answer - Two -digit number are formed , with replacement, from the digits 0-9.

Q: A prime number is a number that is evenly divisible only by 1 and itself. The prime numbers less…

A: Solution

Q: another account Badges Formatting Help Find the sum of all positive integers less than 200 which are…

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Q: Using the set {1,3,4,6,7,8,9}, how many odd numbers can we construct between 100-999 if no element…

A: An odd number is determined by the unit digit. If the unit digit is an odd number, then the number…

Q: Eucharistic King Academy of Sara, Inc. Learning Module for Mathematics B. Find the sum of the…

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Q: The local seven digit telephone numbers in city A have 227 as the first three digits. How many…

A: Given that: Local 7 digit telephone numbers in a city A have 227 as the first three digits.

Q: discrete math How many 5 digit numbers can be written with the digits {1, 2, 3, 4, 5, 6, 7, 8} if…

A: Given set of digits={1,2,3,4,5,6,7,8}  number of digits in main set n=8 We have to make 5-digit…

Q: Answer permutation problem completely. Show complete solution. How many 4-digit numbers can be…

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Q: Fill in the blanks: Consider the numbers 2, 4, 5, 7 and 8. If repetition is not allowed, how many…

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Q: 3. True or false? If a number is divisible by both 3 and 9, then is must be divisible by 27.

A: Solution

Q: 3.50. How many three-digit numbers are there with different digits and at the same time: (a) odd b)…

A: Given problem Given that   How many three-digit numbers are there with different digits and at the…

Q: I am an odd number I am divisible by 3 what number am

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Q: In how many different ways can five people be seated in a row if two of them insist on not sitting…

A: Given that  In how many different ways can five people be seated in a row if two of them insist on…

Q: xercise 4. Let a, b, c be integers. Show that if [a]n = [b]n, then [ac], = [bc],n.

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Q: The natural numbers are l PEN N={1,2,3,...). The prime numbers are P= {2,3,5,7...}. True or false?…

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Q: (a) Let n 6,409. How many prime numbers are less than or equal to the square root of n? Is n…

A: Value of square root of 6409 is approx 80

Q: How many 3-digit numbers with no repeated digits contain a 3, but no 6 and no 7?

A: The 3 digit numbers with no repeated digits. There are 10 digits from 0-9.

Q: a + (-a) = : The sum of a real number and its additive the additive

A: a+(-a)=_______: The sum of a real number and its additive_______is _______, the additiive________.

Q: R.3. Given 8 different natural numbers, none greater than 15, show that at least three pairs of them…

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Q: The natural numbers are N= {1,2,3,..}. The prime numbers are P = {2,3,5,7...}. True or false? ØSN…

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Q: The natural numbers are N= {1,2,3,.}. The prime numbers are P = {2,3,5,7..}. True or false?…

A: The given set of natural numbers and primes numbers are ℕ=1,2,3,... and ℙ=2,3,5,7,... respectively.…

Q: The product of an odd and an even number is an even number. Consider 15 and 36. What conclusion can…

A: A number is said to be odd if it is not a multiple of 2. A number is said to be even if it is a…

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.