b) How many three-digit phone prefixes are possible in which no digit appears more than once in each prefix? c) As in part (a), how many three-digit phone pre- fixes are possible that do not start with 0 or 1, but contain 0 or 1 as the middle digit?

Q: How many different possible area codes are there if an area code is 3 digits long and cannot contain…

A: From the provided information, An area code is 3 digits long and cannot contain a 0 or have 1 or 9…

Q: first digit of the phone number can not be a U?

A: Given 10 digit phone numbers are there in Montana with an area code of 406 the first digit of the…

Q: A catalog begins with three dlistinct letters +ollowed by four distinct nonzero digits. what is the…

A:

Q: 13. Prove that if the sum of digits of a number is divisible by 9, then so is the number.

A:

Q: How many four-letter code words are possible using the letters in IOWA if, (a)The letters may not…

A:

Q: In certain state, all license plates consist of from four or five symbols chosen from the 26 letters…

A: We need to find the number of license plates in which repetition of symbols is not allowed. The…

Q: Suppose the Department of Motor Vehicles uses six digits and the numbers 0 through 9 to create its…

A: Solution.

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: There are total 7 digits, such that, 2, 3, 4, 5, 6, 7 and 8.

Q: How many different license plates are possible if a state issues, (a) Two letters followed by a…

A: Here we have to find How many different license plates are possible if Two letters followed by a…

Q: Suppose we want to form four-digit numbers using the set of digits {0,1, 6, 7, 9}. For example, 9071…

A: The first number can be selected in 4 ways. [ Any number from {1,6,7,9} ] The second number can be…

Q: 2) The Venn diagram shows how real numbers, rational numbers, irrational numbers, integers, and…

A: Venn Diagram: Euler Venn Diagram or commonly known as Venn Diagram, is a diagrammatic representation…

Q: Which of the following is FALSE about the relationship between whole numbers and rational numbers? O…

A: We are given 4 statements regarding knowledge in whole number and rational numbers. We need to find…

Q: How many odd integers from 1,000 through 9,999 have distinct digits?

A: From 1000 to 9999 , all are 4 digited integers.  If the integer is odd then the last digit can occur…

Q: Assume a country has 3-digit area codes that all have 0 or 1 as the middle digit, do not have 0 or 1…

A: Solution: From the given information, 3-digit area code should be formed. The first digit do not…

Q: How many numbers between 3000 and 4000, with distinct digits, can be formed using the    digits 1,…

A:

Q: Before 1995, area codes for phone numbers had the following format: NNN, where first digit couldn’t…

A: Given that , Before 1995, area codes for phone numbers had the following format: NNN where (1) first…

Q: How many whole numbers are there with exactly 5 digits that can be written using only the digits 8…

A: no. of whole number possible with exactly 5 digits from digits 8 and 9 = ?

Q: How many posible 5-digit zip codes exist if the first number must be from 3 and 9, the last number…

A: We have given that 5-digit zip codes exist if the first number must be from 3 and 9, the last number…

Q: In how many ways can a 4-letter code word be formed from the letters of the word CHECKBOOK?

A: Please comment down for any doubt. I hope my answer helps you.

Q: In how many distinct ways can a 18-digit number be made using nine 9's and nine 9's?

A: We have to find the distinct ways a 18-digit number be made using nine 9's and nine 9's.

Q: How many ways to arrange 7 books on the shelf exist if two definite books are not placed together?

A:

Q: How many ways are there of arranging the 26 letters of the alphabet so that none of the words be,…

A:

Q: To use an automated teller machine at a certain bank, you must enter a 4-digit code, using the…

A: Total available numbers = 9 To make 4 digit code

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: 23 Find the number of permutations of all the letters of the word NOTEPAD if: a) the letters can be…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: A word given as “FATİHSULTANMEHMET”. If we fix ‘FATİH’ in this sentence, how many different words…

A: FATİHSULTANMEHMET can be Rearranged as (Total number of letters)!(Total repetitions of any letter)!

Q: Until recently, all area codes had a 0 or a 1 as the middle digit and the first digit could not be 0…

A: Given that a phone number consist of 3-digit area codes followed by sequence of 8-digit numbers. (a)…

Q: How many six-digit even numbers more than 200,000 can be formed using all of the digits 1, 1, 2, 2,…

A: Step 1: Step 2: Step 3: Step 4:

Q: In how many integers greater than 0 and smaller than 10000 digit 5 appears exactly once?

A:

Q: In one state the license plate “numbers” consist of three numerical digits followed by two upper…

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

Q: How many 10 digit phone numbers, Area code + number (***)***-****, are possible if the second digit…

A: Total 10 digit number are possible are, the first digit can not be '0' so it has '9'…

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: 11. How many 7-digit numbers are even or have exactly three digits equal to 0?

A: let X be the set of 7-digit even numbers.

Q: Can the accidental transposition of two consecutive digits in an airline ticket identification…

A:

Q: There are 29 students in precalculus; in how many ways can students fill the Top five?

A: Permutation: A permutation is an arrangement of objects in a definite order.   Let n is the total…

Q: How many 3-digit numbers with digits in {1,..., 9} (repeats allowed) are divisible by 9?

A: Given digits are 1,2,3,4,5,6,7,8,9. Make three digit numbers using the given digits. To find: The…

Q: Consider integers from 1,000 to 9,999. Then, answer the following questions. a) How many even…

A: From 1000 to 9999 all are 4 digit numbers , So we need to filled up four places to get the number .…

Q: How many three digit numbers (values between 100 and 999 inclusive) are divisible by four? How many…

A: