3.73 How many seven-digit numbers with different digits belonging to the set ${3,4,5,6,7,8,9}$ and simultaneously: (a) smaller than 5000000 b) greater than 6500000 ?

Q: How many different 5-digit even numbers can be formed from 0, 1, 3, 4, 5, 7, and 9 if repetitions…

A: The digits used to form the 5-digit even numbers is 0, 1, 3, 4, 5, 7, and 9.

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: 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: 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: 4. How many different 9-digit numbers can be formed by using the digits in the number 277,728,788?

A: Given numbers  277,728,788 Here we need to evaluate many different 9-digit numbers that can form by…

Q: How many positive integers less than 1,000,000 have a digit sum of 5?

A: We have to find the number of positive integers 1,000,000 have a digit sum of 5. The number less…

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: How many even 4-digit numbers can be formed from the digits 1, 2, 6, 7, and 9 with no repetitions…

A: There is no repetition allowed.. At unit place we have two choices 2 or 6 In 10th place we have…

Q: How many numbers between 1234 and 1234567 are of 5? multiples of 2 or multples

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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: If repetitions are not permitted, how many 3-digit even numbers can be performed from the six digits…

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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 (including leading 0s)are there with no digit appearing exactly two times?

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

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Q: In how many distinct ways can a 18-digit number be made using nine 9's and nine 9's?

A: We have to find the distinct ways a 18-digit number be made using nine 9's and nine 9's.

Q: How many 5-digit numbers can be created such that no digit is repeated?

A: We need to create 5 digit number  Total digit = 10 ( 0 - 9) 0 cannot be the first digit  1st digit =…

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 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: How many integers between 10000 and 1000000 have no digits other than 5, 7 or 9. How many have no…

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Q: How many numbers can be made each using all the numerals in the set S = {1,2,2,3, 3, 3, 0}

A: According to the provided information, The set are S= {1, 2, 2, 3, 3, 3, 0}

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: Given two natural numbers a and b, how would you check whether a/b has a terminating decimal…

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Q: How many 4-digit numbers greater than 5000 can be formed from the digits 2, 4, 5, 7, 8, and 0?…

A: How many 4-digit numbers greater than 5000 can be formed from the digits 2, 4, 5, 7, 8, and 0?…

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: How many three digit numbers (values between 100 and 999 inclusive) are divisible by four? How many…

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