A set of 32761 pigeons flies home, each to one of 14 gigantic pigeonholes. What is the smallest number of pigeons possible in the pigeonhole that contains the most number of pigeons? Give an exact integer. No credit for being close (that indicates a misunderstanding of the concept).

Q: A four-digit house number contains no zeros. The number has exactly three distinct digits. How many…

A: It is given that a four digit house number has no digits. The number has exactly 3 distinct digits.…

Q: It is desired to write a 3-digit number using the numbers 2, 3, 4, 5, 6, 7, 8. If each number is…

A: Given data: The total numbers are n=7. Case-1 The total 3 digits numbers that can be formed from the…

Q: How many 6-character license plates are possible if the first character must be a letter that is not…

A:

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: t is desired to write a 3-digit number using the numbers 2, 3, 4, 5, 6, 7, 8. If each number is used…

A: Given Information: It is desired to write a 3-digit number using the numbers 2, 3, 4, 5, 6, 7, 8.…

Q: A number is called “quadary” if each digit is either 0, 1, 2, or 3. How many different 5-digit…

A: Given that a number quadary if each digit is either 0,1,2 or 3. To find the number of  different…

Q: if these five numbers form a pattern such that the differernce between each pair of numbers is the…

A:

Q: How many six-digit even numbers are possible if the leftmost digit cannot be​ zero?

A: From the given information,Sample space = {0,1,2,3,4,5,6,7,8,9}It has been given that the leftmost…

Q: How many zeros does 25! end with?

A: A number will have trailing zeros when 5 and at least one even number are factors of it.   Also, the…

Q: For discrete mathematics, show how to find the greatest common divisor of any two numbers

A: For discrete mathematics, show how to find the greatest common divisor of any two numbers.

Q: To answer this question, you will need to (a) create an integer based on the leftmost digit in your…

A:

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: Give an example of a number that is an integer, a whole number, and a natural number ?

A:

Q: The total curb weight of a truck, a car A, and a car B is 11,250 lb. The weight of car A is 15 lb…

A: Given,The total weight of a truck, car A and car B is 11,250 lb. The weight of car A is 15 lb less…

Q: Some states have a single area code for the entire state. Two such states have area codes where one…

A: The sum of two codes is 1203.  To find the two codes.

Q: determine the number of five-digit integers that contains the digit six exactly once

A: Explanation of the answer is as follows

Q: A realtor uses a lockbox to store the keys to a house that is for sale. The access code for the…

A: The total number of digits =10(from 0 to 9) There are 5 digits (1,3,5,7,9) and 5 even digits…

Q: If the largest of 89 consecutive integers is 327, what is the smallest?

A: It is given that largest to the 89 consecutive integers is 327. We need to find the smallest integer…

Q: It is desired to write a 3-digit number using the numbers 2, 3, 4, 5, 6. If each number is used only…

A: Given: Numbers used = 2, 3, ,4, 5, 6 Numbers greater than 530 is required to be found. No digit is…

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

A:

Q: Can a number N, sum of whose digits is 21345, be a square of a natural number?

A: Given: a number N, sum of digit is 21345

Q: How many 4-digit numbers are there?   And if repetition of digits is not allowed?

A: Given that n= number from 1 to 9 = 9 r = 4 ( since we have to take 4 digit number)

Q: In 2020, the pandemic caused by COVID-19 has created havoc all around the world. In a small island…

A: Number of people residing in the island: 1200000 Number of infections per day: 30 Total number of…

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

A: To Find: Number of integers that must be picked in order to be sure that at least two of them have…

Q: A "S number" is a positive even number that is not the product of two even numbers. A "B number" is…

A: Given: S number= positive even number that is not the product of two even numbers,  B number=an…

Q: Some students have difficulty comparing decimals with 0 or comparing decimals that have zeros in…

A: Consider the provided question, Hello. Since your question has multiple sub-parts, we will solve…

Q: A letter that represents a variety of different numbers is called a/an

A: Fill in the blank.

Q: How many distinct ways are there to arrange 3 clear marbles, 4 yellow marbles, and 2 orange marbles…

A: Given problem:- How many distinct ways are there to arrange 3 clear marbles, 4 yellow marbles, and 2…

Q: How many six digit numbers can be formed with no repetitions?

A: We can use all the 6 digits without repetition A 6 digit number cannot have  0 in the first place.…

Q: If the largest of 89 consecutive integers is 327, what is the smallest?

A:

Q: A retailer uses a lock box to store the keys to a house that is for sale. The access code for the…

A: Given Lock box consist of no.of digits=6Total no.of digits =10                   (i.e.,…

Q: A certain website requires a password to be 6 characters in length. Two of the characters must be a…

A: From the provided information, A certain website requires a password to be 6 characters in length.…

Q: There are 12 black socks, 15 dark brown socks, and 20 dark blue socks in a drawer. It is dark and…

A: In a drawer, The number of Black Socks = 12 The number of Dark Brown Socks = 15 The number of Dark…

Q: Given two natural numbers a and b, how would you check whether a/b has a terminating decimal…

A:

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

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

Q: You need to create a four digit code. You can use the digit 035. The first is it cannot be zero. And…

A: We have to find given no. Of arrangement.