1- The total number of positive integers that can be formed from the digits 1,2,3 and 4 if no digit is repeated in any one integer is 24. O True O False

Q: Suppose 35 cars start at a car race. In how many ways can the top 3 cars finish the race?

A: The information provided in the question are as follows :-There are  cars at a car race.

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

A: In this question, concept of combination is applied. Combination A combination is a mathematical…

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: How many 5 digit even numbers are there, a. Given that the first digit cannot be zero. b. Given…

A: In five digit following digit can be filled in following ways: First digit can be filled by…

Q: Select 8 different numbers from {1, 2, 14). Show that you can find at least three pairs of numbers…

A: To show that you can find at least three pairs of numbers with the same positive difference from the…

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: 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: Texas is starting a lottery game. Play- ers use a machine that randomly selects 7 distinct numbers…

A: To calculate the probability that Texas will lose money, we need to determine the expected value of…

Q: How many 5 digit even numbers can be formed from the digits 1, 2, 3, 4, 5 if no repetition is…

A:

Q: How many integers between 1 and 822 inclusive are divisible by 5 or 3?

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Q: How many 3-digit numbers can be formed from the digits 2, 3, 4, 6, 7 without repetitions? b. How…

A: The 3-digit numbers that can be formed from the digits 2, 3, 4, 6, 7 without repetitions are: 234,…

Q: Arealtor uses a lock box to store the keys to a house that is for sale. The access code for the lock…

A: The access code contains 4 digits          Digits : 0,1,2,3,4,5,6,7,8,9 The first digit can…

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

A:

Q: 14. The digits 6, 2, 3 and 8 are each written on a separate sheet of paper. The number of 2-digit or…

A: The total possible two-digit numbers are given by the value of 4P2. Total possible two-digit numbers…

Q: How many integers must you pick in order to be sure that at least two of them have the same…

A:

Q: How many different numbers with nonrepeating digits from 4000 to 6000 can be produced using the…

A: The problem can be solved using the concept of permutation and combination.

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

A:

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

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Q: How many integers between 100 and 999 inclusive are multiples of 13?

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Q: How many distinct four-digit integers can one make from the digits 1,3,3,7,7, and 8?

A: How many distinct four-digit integers can one make from the digits 1,3,3,7,7, and 8?

Q: How many ways are there to write a 3-digit positive integer using the digits 1, 3, 5, 7, and 9 if no…

A: The given digits are: 1, 3, 5, 7, and 9. We have to find the number of ways to write a 3-digit…

Q: 21 and 24 are not relatively prime numbers

A: To find: Whether 21 and 24 are relatively prime numbers or not?

Q: How many integers in between 1 and 3000, inclusive are divisible by either 5 or 7?

A: Let A and B are two sets such that then number of elements in A and B are obtained as…

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: Using the digits 0 through 9, find out how many 4-digit numbers can be configured based on the…

A: The fundamental counting principle says that if there are n ways to choose something and m ways to…

Q: Find the number of different 7-digit numbers which can be formed from the seven digits 4, 4, 7, 9,…

A:

Q: How many four-digit numbers can be formed from the digit 0, 1, 2, 3, 4,5, 6, 7, 8 ,9 if each digit…

A: here available digits are 0, 1, 2, 3, 4,5, 6, 7, 8 ,9 so total 10 digits available here each digit…

Q: How many four digit codes can be made out of the digits 0,2,4and 8 if the repetition of digits is…

A: We have to find four digit codes can be made out of the digits 0,2,4and 8 ....

Q: Which of the following is an Integer ?

A: Given,           Ingeger number.

Q: Bob owns 7 different books. He wants to arrange all of these books left-to-right on a single…

A:

Q: How many different 3-digit numbers can be formed from the digits 1, 3, 4, 5, 6, 7,9 if repetition of…

A: