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. о True O False

Q: Explain why, in any set of 11 positive integers, some two integers must have the same I's digit.

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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: 3) If every student in a class of 12 students gave a high-five to every other student, write an…

A: We have to find how many high-fives occurred in the class.

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: 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: The number of integers between 1 and 500 (both inclusive) that are divisible by 3 or 5 or 7 is

A:

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 can four digits be formed using the digits 0, 1, 2, and 3 (repetition is allowed)? * O 12 O…

A:

Q: A fair die is rolled seven times. Calculate the probability of obtaining exactly two 3s.

A: here given ,  fair die is rolled 7 times  n=  7 here for fair die , possible Outcomes 1,2,3,4,5,6…

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 4-digit numbers can be formed from 0, 1, 3, 5, 7, & 9 if repetition of digits is NOT…

A: Solution-: How many 4-digit numbers can be formed from 0,1,3,5,7 and 9 if repetition of digits is…

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

A:

Q: If the first even integer is 4, then what will be next three consecutive even integers ? O 5, 14, 10…

A: In the question it is asked to represent next three consecutive even integers after even integer 4.

Q: Find 2 5-A O A-8 © 8. A O If A =

A:

Q: Find the number of positive integers not exceeding 104 that are not divisible by 5 or by 7.

A: In this Question we have to find the number of positive Integer between 0 and 104 which is not…

Q: 1- The total number of positive integers that can be formed from the digits 1,2,3 and 4 if no digit…

A:

Q: How many integers between 1000 and 9999 inclusive are not divisible by 5?

A: The number of integers from 1 and 9999 which are divisible by 5 is = [9999 ÷ 5] = [1,999.8] = 1999…

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 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: The number of integers between 1 and 500 (both inclusive) that are divisible by 3 or 5 or 7 is

A: Number of integers between 1 and 500 divisible by 3 = n(3) = 166 divisible by 5 = n(5) = 100…

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

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Q: 57. We have data from 100 economists in academics, private sector, and government ncerning their…

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 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: .Prove that if n is an odd number then 3n + 1 is an even number. Use direct proof. 2.Prove that…

A: Given n is odd number

Q: Which of the following is an Integer ?

A: Given,           Ingeger number.

Q: Is 2 • 3 • 5•7•11•13•17•19 + 1 prime or composite

A:

Q: If an integer n is odd, then n2 + 2n +1 is even. Select one: True O False

A: Given n is odd Now n2 + 2n + 1 = (n+1)2

Q: A committee of 6 U.S. senators is to be formed with 3 Democrats and 3 Republicans. In how many ways…

A: It is given that Number of Republicans = 66 Number of Democrats = 34 To be selected = 6