A sequence of positive integers starts with one 1, followed by two 2s, three 3s, and so on. (Each positive integer n occurs n times.) How many of the first 105 numbers in this sequence are divisible by 3?

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: How many distinct expressions exist for the number?

A: The concept of "distinct expressions" for a number can vary depending on what you mean by it. Here…

Q: Think about the three-digit numbers that can be formed from the digits 1, 2, 3, 4 and 5 without…

A: Solution

Q: Using the digitd 3, 4, 5, 6, 7, 8, and 9, how many 4-digit numbers can be constructed if the number…

A: Solution: From the given information, the digits are 3, 4, 5, 6, 7, 8 and 9. Here, the numbers with…

Q: (a) Find the number of integers between 32 and 395 that are divisible by 6. (b) Find their sum.

A: (a) The first term of the integers between 32 and 395 is a1=36 which are divisible by 6   and the…

Q: How many numbers greater than 3000 can be form with the digits 0,2,3,4 a.  if repetition is not…

A:

Q: How many 3-digit numbers can we make using the digits 2, 3, 4, 5, and 6 without repetitions?

A: here available digit 2,3,4,5 and 6 total 5 digits available

Q: Find the sum of n terms of an AP whose nth term is given by an=5-6n

A:

Q: A team composed of two grade 11 and two grade 10 students is to be sent to a debate contest. If…

A: The provided information is  There are Two grade 11 and two grade 10 students  There are also 60…

Q: How many multisets can we make using the integers 1 through n, if we require that no number appears…

A: It is given that the integers are from 1 through n, and no number appear more than 3 times.

Q: integers

A:

Q: How many ways can 4 books be arranged on a shelf if the books are selected from a collection of 100…

A: Here we will use the concept of permutation Permutation = nPr = n!/(n-r)!

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

A: Given information- We have given the digits- 2, 3, 5, 6, and 9. We have to form the 3 digits numbers…

Q: In how many ways can the numbers from 7 to 10 be arranged three at a time if the numbers can repeat?

A: If we have n numbers and we want to arrange k of them where the numbers can repeat, then the total…

Q: How many different two-digit numbers can you form using the digits 3, 8, 7, 4, 1, and 5 without…

A:

Q: How many 3-digit numbers can be formed from the digits 2, 3, 4, 6, 7 without repetitions? b. How…

A: The 3-digit numbers that can be formed from the digits 2, 3, 4, 6, 7 without repetitions are: 234,…

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

A:

Q: c) List vertically all the ways each number 0-35 can be represented as a sum of two or more…

A: Assume that limiting the numbers to integers. Let's try a few and see if we can find a pattern:…

Q: How many numbers between 1 and 10000 have the digits 1,3, and 5 such that each digit appears exactly…

A: Here Numbers between 1 and 10,000 have digits 1,3,5 and each appears exactly once only

Q: 14. The digits 6, 2, 3 and 8 are each written on a separate sheet of paper. The number of 2-digit or…

A: The total possible two-digit numbers are given by the value of 4P2. Total possible two-digit numbers…

Q: Among all the numbers between 40000 and 90000, including the numbers 40000 and 90000, how many each…

A: The total number of numbers between 40,000 and 90,000 is 90,000-40,000+1=50,001. First calculate the…

Q: How many integers must you pick in order to be sure that at least two of them have the same…

A:

Q: Four numbers are selected from the following list of numbers: -5, -4, -3, - 2, -1, 1, 2, 3, 4; in…

A: Given:  Numbers available : -5, -4, -3, - 2, -1, 1, 2, 3, 4   Aim:  To select 4 numbers out of the…

Q: How many 4 digit numbers can be formed using only the numbers 3 2 7 6 0 4 9 if the number is odd and…

A: numbers: {3,2,7,6,0,4,9} make 4 digit numbers  no repeatation odd numbers: last digit must be odd.…

Q: How many distinct four-digit integers can one make from the digits 1,3,3,7,7, and 8?

A: How many distinct four-digit integers can one make from the digits 1,3,3,7,7, and 8?

Q: For how many n = {1, 2, ..., 695} is n a multiple of one a multiple of one or more of 8, 3, or 7?

A: In the range of [1, 695] the number of numbers divisible by an integer k =  represents the floor…

Q: How many different three-digit numbers can be formed using the digits 1, 5, 9, 7, 4, 8, and 6…

A:

Q: For how many n = {1, 2,…, 645} is n a multiple of one or more of 8, 7, or 3?

A: n belongs to (1,2,....645) is n a multiple of one or more of 8,7 or 3.

Q: that if 3 divides the sum of the digits of n, then 3|n

A:

Q: Sum of odd integers from (8-26) How many 4 digit combination can you make from number 0-9

A: There is no such introduction for the solution.I have explained it within the solution.Please go…

Q: For which values of n does n! have n or fewer digits

A: Solution is as follows

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

A: here available digits are 0, 1, 2, 3, 4,5, 6, 7, 8 ,9 so total 10 digits available here each digit…

Q: How many different three-digit numbers can be formed using the digits 1, 4, 5, and 9 without…

A: Given N=4 n=3