Suppose I choose two numbers from the set {1, 2, 3,… 100}. How many have an even sum? Show all work.

Q: How many outfits can be made from 4 pairs of slacks, 5 shirts, and 3 ties, if one selection from…

A: First decide on a pair of slacks.For that there are 4 different choices.Now for each of those…

Q: Consider 2 classes, the first with 5 students, and the second with 7 students. From this group of…

A: Given data 2 classes First with 5 students and second with 7 students 2 students need to be selected

Q: Suppose a mail carrier must deliver 10 different letters, one to each house on the same street. The…

A: The formula of permutation is: Given: n=10   The required arrangements is calculated as: At least…

Q: Suppose that in a class, there are n many boys and n many girls. Among these 2n many people, we will…

A: Let A be a set of n elements. To select r objects from a collection of n elements in the set A…

Q: Suppose that 54% of people own dogs. If you pick two people at random, what is the that they both…

A: Given: P(Dog) = 0.54 The probability that they both own a dog can be calculated as: P(Both own a…

Q: How many possible results are there that A finished the first, B finished the second, and C finished…

A: SIX STUDENTS ARE SELECTED TO RUN 100 METER SPRINT. ASSUME THAT THEY ARE EQUALLY GOOD AND RESULT ARE…

Q: In how many ways can you distribute n pennies to k children if each child is supposed to get at…

A:

Q: Suppose a set of 8 numbers are selected from the set: {1,2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14}…

A:

Q: How many ways that two girls and 4 boys can fall in a line of there must be a girl and a boy in the…

A: Let us assume there are three persons A, B and C sitting beside each other. The different ways in…

Q: Use any method, list all the three digit numbers from the set {3,4,5,6} where there are no repeating…

A:

Q: Suppose that 4 Pistons need to be installed in a new engine block. there is a production run of 100…

A: Given, there is a production run of 100 Pistonsand 4 Pistons need to be installed in a new engine…

Q: How many numbers must be selected from the set {2,4,6,8,10,12,14,16,18,20} to guarantee that at…

A: Use the principle of inclusion and exclusion to solve this problem, as in next step.

Q: How many numbers must be selected from the set {1, 2, 3, 4, 5, 6} to guarantee that at least one…

A: To find  How many numbers must be selected from the set {1, 2, 3, 4, 5, 6} toguarantee that at least…

Q: How many pairs of two distinct integers chosen from the set {1, 2, 3,..., 101} have a sum that is…

A: Since you have posted multiple questions and we can answer one question. So answer provided for the…

Q: suppose repetitions are not allowed. Find the number n of three-digit even nimbers that can be…

A: Given problem Given that   Suppose repetitions are not allowed. Given six digits : 2,3,5,6,7,9…

Q: Show that if seven integers are selected from {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}, there must be…

A:

Q: What is the sum of the first 150 positive integers?

A:

Q: In how many ways can 25 identical doughnuts can be distributed to 4 police officers so that each…

A:

Q: Suppose 82 jelly beans are distributed among 9 kids, with some kids possibly getting none. Fill in…

A:

Q: What is the sum of the first 200 positive integers?

A:

Q: Each customer in a certain bank has a PIN number, which is a sequence of four digits. Show that if…

A:

Q: In how many ways can 25 identical donuts be distributedto four police officers so that each officer…

A:

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: Registrants at a large convention are offered 6 sightseeing tours on each of 3 days. In how many…

A: Number of sightseeing tours for one day are 6. Number of days for the tour is 3.

Q: If the mean of 5 positive integers is 15, what is the maximum possible difference between the…

A:

Q: How many ways are there to list the digits 1, 1, 2, 2, 3, 4, 5 so that the digit 3 and 4 are not in…

A:

Q: How many three – digit numbers greater than 300 can be formed with the digits 1, 2, 3, 4 and 5 if no…

A: According to the provided information, The digits are 1, 2, 3, 4, 5 and no repetitions are allowed?…

Q: How many pairs of two distinct integers chosen from the set {1, 2, 3, 101} have a sum that is even?

A:

Q: Each prize winners will be randomly selected from 25 people attending a party. There will be 1st,…

A: here given there are total 25 people and total 8 prize are there  here use counting Principle

Q: | Suppose 10 ducks and 6 geese line up in a single row. In how many ways can they line up so that no…

A:

Q: How many numbers must be selected from the set {1, 2, 3, 4, 5, 6, 7, 8} to guarantee that at least…

A:

Q: The total number of positive integers that can be formed from the digits 1,2,3 and 4 if no digit is…

A: Number of possible arrangement can be calculated either by combination or permutation methods.…

Q: How many three-digit numbers is there such that when the middle digit is removed they become a…

A: Let the three digit number be xyz. then on removing the middle digit, the two digit number will…

Q: 20) Show that the sum of two consecutive integers is always odd.

A: Let x be any integer. Then its consecutive integer can be written as x+1.

Q: A committee of 3 is to be formed from a group of 20 people. How many different committee are…

A: A committee of 3 is to be formed from 20 people. So there has to be 3 selections from 20 people…

Q: Suppose person X was infected by a virus and it gets to infect three persons in a day. Each of these…

A: Suppose person X was infected by a virus and it gets to infect three persons in a day. Each of these…

Q: How many three-digit numbers can be formed using the digits 2,3,4,5,6,and 8, if the number is to be…

A: Given:  The provided digits are 2, 3, 4, 5, 6, and 8. The repetition of digits is not allowed. For a…

Q: If n EN and n < 2000, how many numbersn have the property that the sum of the digits of n and the…

A:

Q: Show that if any 14 numbers are selected from the set S = {1,2,3,...,25}, [14] there are at least…

A: Note that the numbers in each of the first twelve sets sum to 26, and that there is no pair of…

Q: How many sequences of 6 positive digits (1-9) contain at least one digit that appears twice?

A: We have to determine the total sequences of 6 positive digits (1-9) that contain at least one digit…

Q: Eight men and seven women are randomly assigned distinct numbers from 1 to 15. On an average, how…

A: Given: The distinct number given 1 to 15

Q: In a lottery, each ticket has 5 one-digit numbers 0-9 on it. (with no digit repeating twice) You…

A: given:- In a lottery, each ticket has 5 one-digit numbers 0-9 on it. There are 10 digits to be taken…

Q: How many sequences of 6 positive digits (1-9) contain at most one even digits?

A: Given number of digits in each sequence=6. Number of digits which can be used=1-9 Number of even…

Q: A certain type of push-button door lock requires you to enter a code before the lock will open. The…

A: Since there will be 4 digits in the entry code and each must be different, the first digit can be…

Q: Red and blue ceramic tiles are laid according to a pattern such that for every 22 red tiles used, 3…

A: Given that there are total 300 ties of Red and blue colour .according to pattern every 22 red…

Q: a committe of 5 people is to be chosen from a group of 6 men and 4 women how many committed are…

A:

Q: If n EN and n < 2000, how many numbers n have the property that the sum of the digits of n and the…

A: Given: n∈ℕ And n&lt;2000

Q: A company has 13 employees, and wants to create a team of 7 employees to work on a new project. Th…

A: Given : n = 13  r = 7

Q: In a lottery game, a ticket has a total of 37 numbers to choose from, a player can mark 6 numbers on…

A: Given that, In a lottery game, a ticket has a total of 37 numbers to choose from, a player can mark…

Q: How many even number more than 10 but less than 800 can be formed from the digits 1, 4, 5, 6, 8 and…

A: even number more than 10 but less than 800 can be formed from the digits 1, 4, 5, 6, 8 and 9

Set Theory

Every field in the present world involves a set. The theory of sets was developed by German mathematician Georg Cantor while working on the “problems of trigonometric series”.