How many natural numbers that are less or equal to 1000 and that are not multiples of 3, 5, or 7 exist?

Q: How many different three-digit numbers can be formed using the digits 3,4,8,5,7,1, and 6 without…

A: Given problem:- How many different three-digit numbers can be formed using the digits 3,4,8,5,7,1,…

Q: How many integers between 100 and 400 contain the digot 2?

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Q: The set of all odd numbers between 100 and 110 that are a multiple of 3

A: We need to find the set of all odd numbers between 100 and 110 that are a multiple of 3.List of all…

Q: How many positive integers between 500 and 999 inclusive are not divisible by 5?

A: For this problem, we must recall that to calculate the number of integers in a range of values that…

Q: How many integers between 0 and 500: 1. Have distinct digits? 2. Are divisible by 3? 3. Are…

A: We will answer the first three subparts as per our guideline. Please resubmit the other subparts…

Q: How many 3-digit positive integers exist that when divided by 7 leave a remainder of 57

A: 3 digit positive integers start from 100 and ends with 999. Least positive 3 digit integer which…

Q: How many integers from 1 through 1000 are multiples of 7 or multiples of 4?

A: Let A be the set of integers that are multiples of 7 and B be the set of integers that are multiples…

Q: 1. How many 5 digit positive integers are divisible by 5 and have at least one 6 as their digit?

A: A number is divisible by 5 if the last digit is either 5 or 0. We have to find the number of 5 digit…

Q: How many different​ three-digit numbers can be formed using the digits 3, 6, 1, 7, 8, 2, and 4…

A: How many different​ three-digit numbers can be formed using the digits 3, 6, 1, 7, 8, 2, and 4…

Q: How many six-digit positive integers contain exactly one one, two twos and three treor? How many…

A: First note that here six digit integer can start only with 1 or 2. If it starts with 1 the remaining…

Q: How many four digit positive integers are there that contain the digit 3 and are divisible by 5?

A: A number is divisible by 5, if the unit digit place contains the number 0 or 5. Let m choices to be…

Q: How many integers between 0 and 500: 1. Have distinct digits? 2. Are divisible by 3? 3. Are…

A: Integers between 0 and 500 = 1, 2, 3, 4, ....., 499   Number divisible by 3 = 3, 6, 9, ...., 498…

Q: Using the digits 2, 4, 6, 7 and 9, how many five-digit numbers can be formed if the number is…

A: Given Information: Digits = 2, 4, 6, 7 and 9 To find how many five-digit numbers can be formed if…

Q: How many permutations of the numbers (1, 2, 3, 4, 5, 6, 7, 8, 9} have the numbers 4, 5 and 6 in…

A: So, the numbers 4, 5 & 6 should remain at their natural position and the other numbers can…

Q: How many integers between 1 and 822 inclusive are divisible by 5 or 3?

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Q: How many 5–digit (decimal) integers are there with none of the digits repeated?

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Q: A four-digit number is to be formed from the digits 0, 1, 2, 3, 5, 7, 8, and 9. How many four-digit…

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Q: How many 5 digit even numbers can you form using all of the digits 1, 2, 3, 3, 5? 12 120 24

A: We have given that the digits 1, 2, 3, 3, 5.

Q: A four-digit number is to be formed from the digits 0, 1, 2, 3, 5, 7, 8, and 9. How many four-digit…

A: Given,digits is 0,1,2,3,5,7,8,9

Q: (a) How many four-digit numbers can be formed from the digit 0, 1, 2, 3, 4,5, 6, 7, 8 ,9 if each…

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Q: How many integers greater than 120 but less than 540 are divisible by 5?

A: Given Problem:- How many integers greater than 120 but less than 540 are divisible by 5?

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: How many integers between 100 and 999 inclusive are multiples of 13?

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Q: How many 5 digit numbers can be formed without repeating any digit, from the following digits 3, 4,…

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Q: Show that given any set of 5 natural numbers, there are 3 numbers whose sum is divisible by 3.

A: Let q∈N. Note that, for every q there exists some x∈N and some v∈0,1,2 such that q=3x+v. Now, let…

Q: 4. How many 4-digit numbers that are divisible by 10 can be formed from the numbers 3. 5. 7. 8, 9. 0…

A: Discaimer : 12:31Since you have asked multiple question, we will solve the first question for you.…

Q: How many integers in the set {1,2,3,4, ..., 200} is divisible by at least one of the primes 2, 5 and…

A: Just use inclusion-exclusion principle for three sets.

Q: how many four-digit even numbers are possible if the leftmost digit cannot be zero? repitition is…

A: The question is to find how many 4 digits even numbers are possible if the left most digit cannot be…

Q: How many positive odd integers less than 10,000 can be written using the digits 3, 4, 6, 8, and 0?

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Q: How many positive odd integers less than 10,000 can be written using the digits 3, 4, 6, 8, and 0 if…

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Q: 12 belongs to the set of natural numbers

A: The natural numbers (i.e. counting numbers) are numbers which are used for counting and ordering.…

Q: How many integers between 1 and 10000(inclusive) are divisible by at one of 9, 10, 11?

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Q: How many integers between 100 and 400 contain the digit 2? There are integers between 100 and 400…

A: Numbers between 200 and 299 contains 2 So total integers = 100 Numbers between 120 – 129 contains 2…

Q: ) How many,8-distinct/digit numbers can be formed if the numbers áre amultiple of/5 and contain the…

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Q: How many four-digit even numbers are possible if the leftmost digit cannot be zero? Repitition is…

A: The possible total ten numbers are {0,1,2,3,4,5,6,7,8,9}.Since the left most digit cannot be zero,…

Q: How many can 3 digits be formed using the digits from 1 to 5 if the digit 2 is never there in the…

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Q: How many integers from 1 to 500 are divisible by at least one of  the numbers 3, 4, 5?

A: Given :  Integers from 1 to 500 Total numbers  = 500 So to calculate the number of divisors, we will…

Q: What is the value of the whole number N, if: N ofof of of 100?

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Q: How many positive integers not exceeding 10,000 are divisible by 7, 17, or 23?

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Q: 7. How many positive integers between 100 and 999 inclusive are divisible by 7?

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Q: How many integers in the range 1 to 100,000 inclusive are divisible by 6, 15 or 21?

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Q: 4. How many positive natural numbers less than 1000 are neither divisible by 3 nor 5 nor 7 nor 11.

A: Let U={1,2,3,...1000} n(U)=1000 A={a∈U/ x is divisible by 3}A={3,6,9. . .…

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Q: Find the sum of all  natural numbers between 250 and 1000 which are exactly divisible

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Q: How many natural number that are less or equal to 1000 and that are not multiplea of 3,5or7 exist

A: To find: Number of natural numbers ≤1000 that are not multiple of 3 or 5 or 7.

Q: a) Using only the numbers 0, 1, 2, 5, 6, 7, and 8, determine how many 4 digit natural numbers are…

A: How many 4 digit natural numbers are possible using 0,1,2,5,6,7,8

Q: How many positive integers between 100 and 999 inclusive are divisible by 7?

A: The formula for term number n in an arithmetic series is . Here, a is the first term, n is the…

Q: How many positive integers between 10 and 99 inclusive are divisible by 2 or 3?

A: How many positive integers between 10 and 99 inclusive are divisible by 2 or 3?

Q: How many corresponding integers are made up of 1443 digits taken from (1-2-3-4-5-6) provided that no…

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Q: How many four-digit positive integers both start and end in even digits:

A: We need to find the number of positive integers both start and end in even digits.