igeonhole Principle Show that in any set of 41 consecutive integers there is exactly one divisible by 41. 2) There are 79 different time slots during which sessions at a college can be conducted. If there are 826 different sessions, how many different rooms will be needed?

Q: How many integers between 100 and 400 contain the digot 2?

A:

Q: How many different passwords of 4 characters can be made using the numbers from 0 to 9 and the…

A: A password of four characters is to be made using the numbers from 0 to 9 i.e. 10 digits and the…

Q: How many 3 digit even numbers can be created if repetition of digits is allowed

A:

Q: How many different passwords are possible? If a cell phone’s password consists of eight characters,…

A: Given that cell phone's password consists of eight characters. first character is 6. The number of…

Q: 5 identical copies of a movie will be stored on 20 computers such that each computer has at most 1…

A: Given: 5 identical copies of a movie will be stored on 20 computers

Q: Show that a number with 30 digits cannot have more than 100 prime factors.  

A: Prime factor: A factor of a number which is a prime number. For example: consider a number 26. The…

Q: How many ways can you get we get a 2 digit passcode if zeros are not allowed?

A: If zero is not allowed, The number of available digits is 9 (1,2,3,4,5,6,7,8,9)

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

A: Solution.

Q: How many natural numbers are there with a maximum of 7 digits, the sum of which is 31?

A: As per the question we have to find the total number of natural numbers between 0 to 9999999 whose…

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

A:

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: Assume that you select digits from the set {2,3,5,7} to form a number between 20 and 700. (1) How…

A: The given set of digits is 2,3,5,7 and the range of numbers is 20 to 700. There would be 2 digit…

Q: Prove that a three-digit number is a multiple of 9 whenever the sum of the digits is a multiple of…

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 any possible arrangement of 8 letters is considered a word and the letters are chosen from…

A:

Q: How many 5-digit numbers (including leading 0s)are there with no digit appearing exactly two times?

A:

Q: How many 5- digit numbers can be formed using the digits 0,1,2,3,4,5,6,7,8,9, if repetitions of…

A: Givendigits = 0,1,2,3,4,5,6,7,8,9No.of digits =10

Q: How many 5-digit numbers can be created such that no digit is repeated?

A: We need to create 5 digit number  Total digit = 10 ( 0 - 9) 0 cannot be the first digit  1st digit =…

Q: How many ways are there to construct a string of 4 digits if numbers cannot be repeated? Asume each…

A: The objective of this question is to find out the number of ways to construct a string of 4 digits…

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: A number with 4 digits is formed from the digits 0, 3, 6, 7, 9 without repetition. How many numbers…

A: Total numbers = 5 Since the 6 and 7 are placed next to each other consider them as a single number.…

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: 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 combination lock has a total of 40 numbers and will unlock with the proper 3-numbers equence. How…

A: Given information- We have given that a combination lock has a total of 40 numbers and will unlock…

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

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 ways are there to construct a string of 4 digits if numbers cannot be repeated? Asume each…

A: The objective of this question is to find out the number of ways to construct a string of 4 digits…

Q: How many different 3-digit numbers are possible using only the digits 1,5,6,7,8 ? How many…

A: We have to find no of ways for make 3 and 4 digit numbers  when repetition allow and not allowed

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