How many 9-digit strings contain at most one 0, and end in a digit that is a square number?

Q: How many 3-digit positive integers exist that when divided by 7 leave a remainder of 57

A: 3 digit positive integers start from 100 and ends with 999. Least positive 3 digit integer which…

Q: A number is called “quadary” if each digit is either 0, 1, 2, or 3. How many different 5-digit…

A: Given that a number quadary if each digit is either 0,1,2 or 3. To find the number of  different…

Q: What is an integer

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: How many six-digit positive integers contain exactly one one, two twos and three treor? How many…

A: First note that here six digit integer can start only with 1 or 2. If it starts with 1 the remaining…

Q: an iPhone locks with a 5-digit code. How many codes are possible, if repetition isnot allowed and…

A: Lock of 5 digit code , Repetition is not allowedFirst digit must be 9 Number of codes = ?

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: Any whole number is divisible by 3 if and only if the sum of its digits is divisible by 3 TRUE FALSE

A: We have to state that the given statement is true or false.   Any whole number is divisible by 3 if…

Q: How many 3-digit numbers can be formed from the digits 2, 3, 5, 6, and 9, which are divisible by 5,…

A: Given information- We have given the digits- 2, 3, 5, 6, and 9. We have to form the 3 digits numbers…

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

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Q: 1. Find the number of zeroes at the end of 100!

A: Introduction :Here, we have asked for the number of zeros at the end of 100 !

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

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Q: 1. How many 10-element multisets can be made from the symbols {1,2,3,4}?

A: Given Elements {1,2,3,4}

Q: Suppose that 75% of students attend lectures for a particular course and 20% of students fall the…

A: Conditional probability : Conditional probability is a measure  of the probability of an event…

Q: Among all the numbers between 40000 and 90000, including the numbers 40000 and 90000, how many each…

A: The total number of numbers between 40,000 and 90,000 is 90,000-40,000+1=50,001. First calculate the…

Q: Suppose that a password is exactly six characters and each character is 1 of the 26 lowercase…

A: The number of lowercase letters is 26 and the number of integers is 10.

Q: A 16-bit string is a sequence of 16 symbols, each symbol a 0 or a 1. How many 16-bit strings are…

A: A bit string is a sequence of  symbols, each symbol a  or a We have to find the possible number of…

Q: An inventory consists of a list of 80 items, each marked "available" or "unavailable." There are 50…

A: Given: Number of items listed is 80, each marked as available or unavailable. There are 50 available…

Q: Let A be the set of all positive integers whose last two digits form a number that is evenly…

A: We have the given condition as   Let us consider A be the set of all positive integers whose last…

Q: how many possible combinations are there for computer password that must contain six letters a…

A: Each of the places can take any letters from A to Z , as no repeat condition is given. Therefore,…

Q: Prove a number is divisible by 3 if and only if the sum of its digits is divisible by 3.

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Q: Show that n-lis divisible by 8, if n is an odd positive integer

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Q: Show that given any set of 5 natural numbers, there are 3 numbers whose sum is divisible by 3.

A: Let q∈N. Note that, for every q there exists some x∈N and some v∈0,1,2 such that q=3x+v. Now, let…

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: identify all natural numbers having exactly 28 divisors.

A:

Q: Prove that a four-digit number is a multiple of 8 whenever the number formed by the first three…

A: The solution is given by using the expanded form of number as follows

Q: For some particular website, the password must start with one of the letters a b or c. Then there…

A: Introduction: As the English alphabet has 26 letters from A to Z, and there are 10 digits from 0…

Q: How many strings of 12 ternary digits (0, 1, or 2) are there that contain exactly hree Os, five 1s,…

A: Strings of 12 ternary digits, 3 possibilities for each digit in the string, gives a total of 3^12 =…

Q: A certain website wants you to build a 6-character password from the letters a through i, the…

A: Given: The letters will be selected from a through i. Thus, there are a total of 9 letters from a…

Q: How many 12-bit strings start with 101 or end with 10 or both?

A: Here the 12-vit string is the string of length 12. And to find the number of specific types of…

Q: A passcode contains four digits from the digits 0-9. How many different passcodes can be made if no…

A:

Q: How many real four digit numbers (they can not start with zero) can be formed from digits 0, 1, 2,…

A: Given digits is 0,1,2,3,4,5,6Total no.of digits = 7

Q: How many zeroes does 188! end with?

A: count number of five's in 188, 5*2=10 . Divide 188 and write quotient again divide quotient again by…

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.