A natural number greater than 1 that is divisible by a number other than itself and 1 is called a/an number.

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: How many odd 4-digit numbers greater than 3000 can be formed from the digits 1, 5, 6, 7 and 8 if non…

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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: How many strings of 1our decimal digits have all four digits that are different? How many strings of…

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Q: How many four digit positive integers are there that contain the digit 3 and are divisible by 5?

A: A number is divisible by 5, if the unit digit place contains the number 0 or 5. Let m choices to be…

Q: In certain state, all license plates consist of from four or five symbols chosen from the 26 letters…

A: We need to find the number of license plates in which repetition of symbols is not allowed. The…

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: In a certain state, each automobile license plate number consists of two letters followed by a…

A: There are 24 choices for each letter. (this explanation was already shown in the image you shared)…

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: How many 5-digit numbers can be formed using the digits 1, 2, 3, 4, 5, 6, 7 if repetition of  digits…

A: It is given that there are six digits 1, 2, 3, 4,5, 6 and 7 and to form five digit number and the…

Q: Assume that you select digits from the set {1,2,3,4,5,7,8} to form a number between 10 and 800. (1)…

A: given set of digits is  {1,2,3,4,5,7,8}  and the range of numbers is 10 to 800. There would be 2…

Q: Assume that you select digits from the set {2,3,5,7} to form a number between 20 and 700. (1) How…

A: The given set of digits is 2,3,5,7 and the range of numbers is 20 to 700. There would be 2 digit…

Q: Find all three-digit numbers with different digits with the property that those numbers are…

A: Let N=100a+10b+c represent all the three-digit numbers, for some digits, a, b and c. Then,…

Q: How many pairs of two distinct integers chosen from the set {1, 2, 3,..., 101} have a sum that is…

A: Since you have posted multiple questions and we can answer one question. So answer provided for the…

Q: How many pairs of integers (a,b) exists such that the product of a,b and HCF of (a,b) is 1080??

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Q: How many different integers must be selected to guarantee that at least 5 of them would have the…

A: Dividing any integer by 3, can have remainder 0, 1 or 2. Therefore, possibilities for remainder are…

Q: Four digit numbers can be formed from the six digits 2, 3, 5, 6, 7, and 0. If repetitions are not…

A: here given , 4 digit number can be formed from the six digits 2,3,5,6,7 and 0 4 digit number can be…

Q: The number of positive integers not exceeding 750 that are divisible by 3. 4. and 7 is: *

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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 ways are there to arrange 3 clear marbles, 4 yellow marbles, and 2 orange marbles…

A: Given problem:- How many distinct ways are there to arrange 3 clear marbles, 4 yellow marbles, and 2…

Q: Compute the sum of the first 50 positive integers that are exactly divisible by 5.

A: To determine sum of the first 50 positive integers that are exactly divisible by 5.

Q: Show that given any set of 5 natural numbers, there are 3 numbers whose sum is divisible by 3.

A: Let q∈N. Note that, for every q there exists some x∈N and some v∈0,1,2 such that q=3x+v. Now, let…

Q: From the digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9, if five-digit numbers are to be formed and…

A: As per our guidelines we are supposed to answer only 3 sub-parts of any one question We have given…

Q: How many 9 digit numbers are there that use each of the digits 1,2,3,4,5,6,7,8,9 exactly once?

A: To form a 9 digit number We know that each 9 digit places are must be one of the 9…

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: How many strings of 7 decimal digits are there, such that at least one of the digit is odd?

A: There are total 10 decimal digits, among which 5 are odd. Since repetition of digits is allowed,…

Q: How many pairs of two distinct integers chosen from the set {1, 2, 3, 101} have a sum that is even?

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Q: = there to construct a string of 4 digits if numbers can be repeated?

A: We have to make a 4-digit number where digits can be repeated. Since the digits of number are not…

Q: How many 3-digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 0, which are divisible by 5…

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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: A five character computer password can be formed from three digits, followed by two lower case…

A: There are totally 26 lower case letters of the alphabets(a-z) and 10 digits (0-9). A five character…

Q: How many integers between 1 and 10000(inclusive) are divisible by at one of 9, 10, 11?

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Q: Find all three-digit numbers with different digits such that those three-digit numbers are divisible…

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Q: A computer password is to consist of three lower case letters followed by two digits. Determine how…

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Q: How many different 3-digit numbers are possible using only the digits 1,5,6,7,8 ? How many…

A: We have to find no of ways for make 3 and 4 digit numbers  when repetition allow and not allowed

Q: How many three​-digit numbers may be formed using elements from the set​{1, 2, 3, 4, 5, 6​} if…

A: Given data: Set{1,2,3,4,5,6} To find: Three​-digit numbers  formed using elements from the set​.

Q: For some particular website, the password must start with one of the letters W, X, Y, or Z. Then…

A: As the English alphabet has 26 letters from A to Z, and there are 10 digits from 0 through 9, total…

Q: How many different words can be formed with the letters of the word ‘SUPER’ such that the vowels…

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Q: A security keypad uses five digits (0 to 9) in a specific order. How many different keypad patterns…

A: There 5 events digits and 5 odd digits. The security keypad uses five digits from 0 to 9. There are…

Q: How many three-digit odd integers can be formed using the digits 0, 1, 4, 5, 6, 7, and 9 only once?

A: Permutation: A permutation of a set is defined as an arrangement of its members into a sequence or…

Q: How many four-digit odd numbers are possible if the leftmost digit cannot be​ zero? There are…

A: From the given information,Sample space = {0,1,2,3,4,5,6,7,8,9}It has been given that the leftmost…

Q: How many four-digit even numbers are possible if the leftmost digit cannot be​ zero?

A: The question is to find how many 4 digits even numbers are possible if the left most digit cannot be…

Q: ) How many,8-distinct/digit numbers can be formed if the numbers áre amultiple of/5 and contain the…

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Q: How many different 3-digit numbers are possible using only the digits 6,7,8,9 ? How many…

A: Given, There are 4 digit, 6,7,8,9

Q: How many three-digit odd numbers are possible if the leftmost digit cannot be zero?

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Q: 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 it has a 0 or 5 in the unit digit place. Let m choices to be made…

Q: Suppose each license plate in a certain state has one digit, followed by four letters, followed by…

A: FORMAT of number = 9AAAA9 (1 number, 4 letters, 1 number) A license plate has six spaces to be…

Q: How many 4-digit numbers are there that are divisible by 10 and the sum of whose digits is 10?

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Q: Consider 4 digit numbers with each digit from the set {1, 2, 3, 4, 5, 6, 7, 8, 9} .  How many such…

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Q: Put a positive whole number in each of the four boxes of this table that satisfies the rule. For…

A: Prime number is a positive integer having exactly 2 factors. for example 7 is a odd prime number as…