Question 8 (a) Use the pigeonhole principle to show that if you randomly arrange the numbers 1–12 around a square, 3 numbers along each side of the square, that the numbers along at least one of the sides must add up to 20 or more. (b) How many friends must you have to guarantee at least 5 of them will have birthdays in the same month. Use the extended pigeonhole principle.

Q: How many arrangements are there of the letters of the word MATHEMATICS in which all the vowels…

A:

Q: Find the number of the permutation of 8 different things taken 3 at a time

A:

Q: How many different photographs are possible if four children sit in the front row and five adults…

A: The objective of this question is to find out the total number of different photographs possible…

Q: A person is 4 years old and his sister is half his age, so if this person is a hundred years old,…

A: Given: Age of the person = 4 years Age of the sister = 2 years (half of that of person's age)…

Q: supermarket wants to send codes for $0.25 off a bag of chips to its rewards program members. Each…

A: Given, a supermarket wants to send codes for $0.25 off abag at chips to its rewards program…

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: A startup business began with eight employees, and its size has been doubling every 13 months. (a)…

A: Given that initial number of employees=8 Double time= 13 months

Q: Find the smallest number n for which n! is larger than the population of the world.

A: World population is 7.98 billion till October 2022 It according to worldometer by United States.…

Q: d the number of permutations of a rectang

A: Concept: Since total number of permutation of choosing "r" points out of "n" point is:

Q: A variable name in the programming language Visual Basic must begin with a letter (uppercase or…

A: It is given that a variable in the programming language VB, should be of 5 characters and should…

Q: An ATM pin consists of 6 digits. Each digit can be numbers 0-9. The PIN should not be a birthdate…

A: Given: Number of digits in ATM pin is, N=6. The possible numbers from 0 to 9 are, n=10. The first…

Q: A supermarket send codes for $0.25 off a bag of chips to its rewards members. Each coupon code will…

A: Number of letters allowed = 24 Number of digits allowed = 7 Each coupon code will have one digit…

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: If it will be allowed to use a number repeatedly, how many 4-digit numbers can we form from the…

A: In this question we have to find how many four digit can be formed from the given numbers.

Q: A die is rolled four times consecutively. Find the number of possible outcomes if the order of the…

A:

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: Any n consecutive integers will include a number that is divisible by n.

A:

Q: Find the number of arrangements of the letters in the word EMERGE in which (a) all the 3 letters E…

A: Given word is EMERGEletter E is repeated 3 times total no.of letters in the word  EMERGE  =6

Q: For the purposes of this problem, suppose that the Bingo master chooses numbers with replacement. a.…

A: BINGO4273255731525415875826059707223354621317434867

Q: Suppose that the number of students in a class increase by 2, the number of ways they may be…

A:

Q: You are given a bag with 40 concert tickets, 5 for each of 8 different concerts. Assume five…

A: If there are n boxes and (n+1) pigeons then, one box out of n boxes will have two pigeons.

Q: Jonah has 10 cards and each card has one of the numbers: 3, 8, 13, 18, 23, 28, 33, 48, 53, 68. What…

A: Given,  10 cards with numbers on them 3,8,13,18,23,28,33,48,53,68  We have to find the least number…

Q: What is the probability that there will be at least 2 N's and exactly 4 B's in the first 12 numbers?…

A: BINGO4273255731525415875826O59707223354621317434867

Q: The average age of the students in Class A is more than 11 years old. If ten out of the eleven…

A:

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

A:

Q: a. The Bingo master starts a new round. What is the probability that the first 3 numbers will be…

A: BINGO4273255731525415875826059707223354621317434867

Q: use your own words to describe the steps of the method of mathematical induction

A: We have to write the steps for method of mathematical induction