If S-[ Integers less than 20) : A-( all Prime Numbers in S) ; B=(Odd numbers in S); C = (Even Numbers in S) What is B'nC? O 1,3,5,7,9,11,13,15,17,19 O 2,4,6,8,10,12,14,16,18 1,2,3,5,7,9,11,13,15,17,19 O None of the above

Q: Produce the least positive number that is divisible by​ 2, 3,​ 4, 5,​ 6, 7,​ 8, 9,​ 10, and 11.…

A: Given Produce the least positive number that is divisible 2, 3,​ 4, 5,​ 6, 7,​ 8, 9,​ 10, 11.…

Q: 1. How many three digit numbers can be formed from the digits 1,2,3,4 and 5 if one is not to used as…

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Q: 1. How many 5 digit positive integers are divisible by 5 and have at least one 6 as their digit?

A: A number is divisible by 5 if the last digit is either 5 or 0. We have to find the number of 5 digit…

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

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Q: A 3-digit code is to be made from the set of digits {4, 5, 6, 7, 8}. a. How many codes can be formed…

A: Given:

Q: a. no three digits are to be the same? b. the number must be odd? c. the number must be even?

A: here given  5 digit number formed from the digits 1,2,3,....9  so there are 9 digit available for…

Q: Using the digits 0,1,2,....8,9 determine how many of each type of the three-digit number can be…

A: Given digits 0, 1, 2, ............., 8, 9 Any three digit number with zero at its first place…

Q: How many natural numbers that are less or equal to 1000 and that are not multiples of 3, 5, or 7…

A: A number is said to be divisible by other number if on dividing the number  with it given remainder…

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

A: Solution.

Q: How many different three digit numbers can be made from the set of integers {1,2,3,4,5,6,7,8,9} if…

A: The set of integers {1,2,3,4,5,6,7,8,9}

Q: If seven integers are chosen from between 1 and 12 inclusive, must at least one of them be odd? Why?

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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: How many permutations of the numbers (1, 2, 3, 4, 5, 6, 7, 8, 9} have the numbers 4, 5 and 6 in…

A: So, the numbers 4, 5 & 6 should remain at their natural position and the other numbers can…

Q: How many 5–digit (decimal) integers are there with none of the digits repeated?

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Q: Let Sbe the set of all (nonnegative) 4-digit integer. How many integers from start with 1 and end…

A: let S be the set of all 4-digit integer. how many integers from start 1 and end with 9

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: 2. even numbers are in their natural positions. Determine the number of permutations of {1, 2, 3, 4,…

A: Here we use combination rules. And set theoretic rules.

Q: 2) How many integers between 1 and 200, including both 1 and 200 are divisible by 4 or 5? 3) How…

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Q: How many positive integers less than 1000 are divisible by 5? How many positive integers less than…

A: We will answer the first three questions as per our guideline. Please resubmit the other question…

Q: 6. How many integers from 1 through 100 must you pick in order to be sure of getting one that is…

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Q: Is the set O of all odd counting numbers (1, 3, 5… ) closed for multiplication? Why or why not?

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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: 2. Let S = {100, 101, 102,...,999} so that [S] = 900. (a) How many numbers in S have at least one…

A: We need to find number of digits.

Q: 11. What is the sum of all 4 digit numbers formed using the digits 2, 3,4 and 5 without repetition?

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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: 11. How many positive 10-digit integers contain no 0's and exactly three 6's?

A: A 10-digit number is obtained by using 0-9 digits. Each digit has the same number of choices if…

Q: How many six-digit numbers can be formed with the numbers 0, 0, 1, 1, 2 and 2? (Note that a…

A: Given, Numbers - 0,0,1,1,2,2

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

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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: 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: 3. How many different 6-digit numbers can be formed from the numbers 25627 2? permutation set up

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