3) Sarah writes down random positive integers when she gets bored. Prove that if Sarah writes 1001 numbers, then there must be at least 2 with the same last three digits.

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: 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: A phone number is a 7-digit that does not start with 0. Call a phone numbers that make up of exactly…

A: According to the permutation rule, if r distinct items are to be chosen from n items without…

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

A:

Q: If ten integers are chosen from between 0 and 21 exclusive, must at least one of them be even?…

A: Pigeon hole principle states that if n objects are put in to m containers with n>m then at least…

Q: If a phone company sends a random 6-digit number to customers to activate their phone, how many…

A: Consider a problem in which there are n vacant inline spots, each spot is to be filled by any of the…

Q: How would I go about answering this question?

A:

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

A:

Q: Suppose that 11 children collected 50 books. Prove by contradiction that at least two of them had…

A: In mathematics, proof by contradiction is a method of proving something by assuming opposite of what…

Q: A box contains 15 balls in which seven are green and eight are yellow. If five balls must be drawn…

A: It is given that Number of green balls = 7 Number of yellow balls = 8 Total number of balls = 15…

Q: nd presently has 3 lots to build on

A: Given : a contractor builds homes of 6 different models and presently has 3 lots to build on.  we…

Q: How many strings of four decimal digits a) do not contain the same digit twice? b) end with an even…

A:

Q: If seven integers are chosen from between 1 and 12 inclusive, must at least one of them be odd? Why?

A:

Q: 4. If each Automated Teller Machine card of a certain bank has to have four different digits in its…

A: Answer is mentioned below

Q: Suppose there seven people at a party. Is it possible that everyone at the party knows exactly three…

A: It is not possible. Imagine constructing an acquaintance graph in which each of the 7 people are…

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: The digits 0, 1, 2, 3, 4, 5, 6 and 7 are used to make 4 digit codes. (a) How many unique codes are…

A: As per Bartleby guideline, if more than three subparts are asked only first three to be answered…

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: A 6-digit phone number cannot start with 0 or 1. Assume that there are no restrictions on the…

A:

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: Suppose that you have a combination lock that uses letters instead of numbers for its combination,…

A: Solution: The total number of letters is 26 and the lock will be opened with four letters and…

Q: A phone number is a 7-digit that does not start with 0. Call a phone numbers that make up of exactly…

A: A phone number consists of 7 -digit that does not start with 0. To find the possible phone numbers…

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

A:

Q: Suppose that 175 heads and 225 tails resulted from 400 tosses of a coin. Does this appear to be a…

A:

Q: Compute P5,4. (Enter an exact number.)

A: Obtain the value of P5,4.  The value of P5,4 is obtained below:   Permutation: A permutation is an…

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 may be formed using elements from the set​{1, 2, 3, 4, 5, 6, 7, 8, 9​}…

A: given:  set ​{1, 2, 3, 4, 5, 6, 7, 8, 9​}   if no element may be used more than once in a number and…

Q: How many three digit passcode can be made from the digits 0-9in the first number is not allowed to…

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

A: Given data: Set{1,2,3,4,5,6} To find: Three​-digit numbers  formed using elements from the set​.

Q: How many 5-digit numbers can be made from the digits 1 to 9 if: a) Repetition of digits is allowed?…

A: Here AS PER POLICY I HAVE CALCULATED FIRST 3 SUBPART ONLY

Q: A security keypad uses five digits (0 to 9) in a specific order. How many different keypad patterns…

A: There 5 events digits and 5 odd digits. The security keypad uses five digits from 0 to 9. There are…

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 4-digit pin codes can be made using the numbers 0 up to 9 if repetition is not allowed and…

A: Solution Total number of digits from 0 to 9 = 10

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: Suppose that 33% of McMaster undergraduate students are in their first year. President David Farrar…

A: It is given that p=0.33.

Q: A contractor builds homes of  11 different models and presently has 6 lots to build on. In how many…

A: We have to find the different ways can he arrange homes on these 6 lots...

Q: To gain access to his account, a customer using an automatic teller machine (ATM) must enter a…

A: We will use basic combinatorics.

Q: 3) Among a group of seven (not necessarily consecutive) integers, how many must be divided by 5 to…

A: This is a problem related to divination rule of the mathematics. Based on the general concept we…

Q: 1. A registration code begins with three numbers. If the possible numbers are 1, 2, 7, 9 and 0, how…

A: We have find on of more..

Q: 5. Show that if there are 30 students in a class, then at least two have last name begin with the…

A:

Q: Suppose that 31% of McMaster undergraduate students are in the first year. President David Farrar…

A: It is given that p=0.31.

Q: If you have 12 boxes then how many balls do you have to put randomly into the boxes in order to…

A: Given that, We are having 12 boxes. In order to have atleast 4 balls in each box when a random box…

Q: Suppose 10 baseball players are available to be drafted by 4 teams where each team might win any…

A: Assume the number of players drafted in 4 teams are x , y , z and w. Total number of players = 10…

Q: If a bank sends a random 5-digit number to customers for security, how many potential numbers are…

A:

Q: 2) How many numbers are there between 6000 and 7000 which have exactly one of their digits as 7?

A: Since, we have to find numbers between 6000 and 7000 so the thousand's place must be occupied by 6.…

Q: How many 3-digit numbers can be formed from the prime numbers from 0 to 10 if the repetition of the…

A: We need to find how many 3 - digit numbers can be formed from the prime numbers from  0  to  10  if…

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

A: “Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…