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

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: 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: Compute the sum of the first 60 positive integers that are exactly divisible by 4.

A: The numbers divisible by 4 is:

Q: How many odd 4-digit numbers greater than 3000 can be formed from the digits 1, 5, 6, 7 and 8 if non…

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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: A natural number greater than 1 that has only itself and 1 as factors is called a/an number.

A: Given that  A natural number greater than 1 that has only itself and 1 as factors is called…

Q: How many strings of 1our decimal digits have all four digits that are different? How many strings of…

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Q: How many five-digit numbers are there for which each digit is either equal to both adjacent ones, or…

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Q: In a set of 2 positive integers, how many ways it can be chosen in less than 50? 1.

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Q: How many four-digit odd numbers less than 5000 can be formed using the digits 2, 3, 4, 5, 6, and 9.

A: Given:  Using the digit 2,3,4,5,6 and 9  We need to find how many four digit odd  number be formed…

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

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Q: How many three digit numbers can be formed from the digits 0, 1, 2, 3, 4, 5, 6 and 7 such that the…

A: To form a 3 digit number, we start we can not place 0 on hundreds position since that will make it a…

Q: The sum of all positive integers less than 300 which are divisible by 3.

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Q: Find all three-digit numbers with different digits with the property that those numbers are…

A: Let N=100a+10b+c represent all the three-digit numbers, for some digits, a, b and c. Then,…

Q: How many different integers must be selected to guarantee that at least 5 of them would have the…

A: Dividing any integer by 3, can have remainder 0, 1 or 2. Therefore, possibilities for remainder are…

Q: How many positive integers less than 1000 (1) are divisible by 7? (2) are divisible by 7 but not by…

A: # As per the guidelines we are entitled to solve three subparts at a time, please resubmit the other…

Q: How many odd integers from 1,000 through 9,999 have distinct digits?

A: From 1000 to 9999 , all are 4 digited integers.  If the integer is odd then the last digit can occur…

Q: How many four​-digit numbers may be formed using elements from the set ​{1, 2, 3, 4, 5, 6, 7​} if…

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Q: How many integers in {1,2, 3, ..., 99, 100} are not divisible by 7? (Give the exact number)

A: The given set of numbers is, 1,2,3,.....,99,100 The total no.of numbers from 1 to 100 is, 100 The…

Q: How many six-digit even numbers greater than 500 000 can be formed using all of the digits 1, 2, 2,…

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Q: Show that, selecting 91 positive integers guarantees that there are at least 10 integers with the…

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Q: The sum of all positive integers less than 300 which are not divisible by 3.

A: Sum of n positive integer is given by, Sn=nn+12

Q: How many integers between 1000 and 9999 inclusive are not divisible by 5?

A: The number of integers from 1 and 9999 which are divisible by 5 is = [9999 ÷ 5] = [1,999.8] = 1999…

Q: How many numbers between 3000 and 4000, with distinct digits, can be formed using the    digits 1,…

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Q: Compute the sum of the first 50 positive integers that are exactly divisible by 5.

A: To determine sum of the first 50 positive integers that are exactly divisible by 5.

Q: show that every integer greater than 11 is the sum of two composite integers

A: We need to prove that  every integer greater than 11 is the sum of two composite integers.

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 three digit numbers can be formed from the digits 0,1,2,3,4,5,6,7,8 and 9 such that the…

A: Given numbers are, 0,1,2,3,4,5,6,7,8 and 9 Total numbers are 10 We have to calculate the number of…

Q: How many 3-digit numbers can be formed from the digits 2, 3, 5, 6, 7, and 9 which are divisible by 7…

A: Given:   Digits: 2 , 3 , 5 , 6 , 7 and 9 3-digit code  which divisible by 7 with no repetition of…

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 strings of 7 decimal digits are there, such that at least one of the digit is odd?

A: There are total 10 decimal digits, among which 5 are odd. Since repetition of digits is allowed,…

Q: How many six-digit even numbers less than 200 000 can be formed using all of the digits 1, 1, 2, 2,…

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Q: How many 3-digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 0, which are divisible by 5…

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

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Q: Find all three-digit numbers with different digits such that those three-digit numbers are divisible…

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Q: How many different 3-digit numbers are possible using only the digits 1,5,6,7,8 ? How many…

A: We have to find no of ways for make 3 and 4 digit numbers  when repetition allow and not allowed

Q: Determine all natural numbers divisible by 8 whose sum of digits is less than 10 and the product of…

A: Permutation and combination concepts will be used to filter out all the 3 scenarios in getting…

Q: How many 3-digit numbers with digits in {1,..., 9} (repeats allowed) are divisible by 9?

A: Given digits are 1,2,3,4,5,6,7,8,9. Make three digit numbers using the given digits. To find: The…

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 three-digit odd integers can be formed using the digits 0, 1, 4, 5, 6, 7, and 9 only once?

A: Permutation: A permutation of a set is defined as an arrangement of its members into a sequence or…

Q: How many different 3-digit numbers are possible using only the digits 6,7,8,9 ? How many…

A: Given, There are 4 digit, 6,7,8,9

Q: How many integers from 1 to 99,999 contain exactly two consecutive 1s?

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Q: 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 it has a 0 or 5 in the unit digit place. Let m choices to be made…

Q: that the set of negative integers divisible by 3 is countable

A: Set of negetivee integers divisible by 3 isS=-3n, n∈ℕf: ℕ→S   defined asf(n) = -3n,To check…

Q: How many four-digit odd numbers less than 5000 can be formed using the digits 2, 3, 4, 5, 6. 6, and…

A: Now here given  digits 2,3,4,5,6,9

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

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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?