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

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Q: 1. How many five-digit numbers can be formed from the digits 3, 4,5,6 and 7? a. no repetition of…

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Q: . How many are greater than 330 in a group of 3 digit numbers forme d 5 where digit (s) may be…

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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: 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

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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: How many different license plates are possible if a state issues, (a) Two letters followed by a…

A: Here we have to find How many different license plates are possible if Two letters followed by 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: 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: Show that if seven integers are selected from {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}, there must be…

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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: How many odd integers from 1,000 through 9,999 have distinct digits?

A: From 1000 to 9999 , all are 4 digited integers.  If the integer is odd then the last digit can occur…

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: 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: 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 numbers between 3000 and 4000, with distinct digits, can be formed using the    digits 1,…

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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: 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: 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 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?

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Q: Recall that hexadecimal numbers are constructed using the 16 digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A,…

A: We know that,Hexadecimal numbers are constructed using the 16 digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 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: 31. How many two digit combination can be formed using digits from 0 to 9? * 041 0 43 0 45 0 47

A: To find: Two digit combination formed using digits from 0 to 9. Formula used: Crn=n!n-r! r!…

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

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Q: 5. How many integers between 1 and 9999 have no repeated digits? How many have at least one repeated…

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