1. Is a set {-22,-15,-9,-2,5,10,25,33,44} modulo 9 a CRS? Why? 2. Is a set {-22,-3,0,1,2,3,4,5,6,7,9,10} modulo 9 a CRS? Why?

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

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Q: How many different passwords of 4 characters can be made using the numbers from 0 to 9 and the…

A: A password of four characters is to be made using the numbers from 0 to 9 i.e. 10 digits and the…

Q: Subject identification numbers in a certain scientific research project consist of two digits…

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Q: How many ways can we choose 3 numbers from the set (1, 2, 3, 4, 5, 6, 7) (The order we choose…

A: Permutation:   It is nothing but the arrangement of items in a definite order where the order is…

Q: We are making 8-letter words from the set of letters a, b, c, d, e, f ..., in such a way that we…

A: Here we will use permutation /arrangement and combination / selection  Number of way r object can be…

Q: For some particular website, the password must start with one of the letters A, B, or C. Then there…

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Q: Queen chooses sixteen different numbers from the set {1, 2, 3,..., 25, 26}. Prove, or disprove, that…

A: There are total 26 numbers in the set  {1, 2, 3,..., 25, 26}. Also the queen chooses 16 different…

Q: In how many ways can four distinct numbers be chosen from the set {1,2,...,14} so that no pair among…

A: solution:- Probability when all four chosen numbers are not consecutive = 1 − Probability when all…

Q: Supposed repetitions are not allowed. Find the number n of three-digit even numbers that can be…

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Q: Is a set {-22,-3,0,1,5,9,10} modulo 7 a RRS? Why? Is a set {-5,-22,-15,-9,-2,5,8,10,25,34,48} modulo…

A: A subset S of the integers is called a reduced residue system modulo n if: gcd(r, n) = 1 for each r…

Q: A number N is divisible by 4 iff the number formed by the last 2 digits of N is divisible by 4. For…

A: We can find number divisible by 4  by using the concept given in the question

Q: Using only the digits { 1, 2, 3, 4, 5, 6} how many three digit numbers can be formed under the…

A: The first digit has 4 options which are, 1, 2, 3, 6. The second digit can have 5 options (one option…

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 natural numbers are there with a maximum of 7 digits, the sum of which is 31?

A: As per the question we have to find the total number of natural numbers between 0 to 9999999 whose…

Q: Find the number of permutations {1, 2, 3,...,8 } such that:   1) Exactly 4 digits in their usual…

A: Total elements= 8  Number of ways in which we can choose the four elements that will be in place is…

Q: The set K of numbers is K={30,32,55,65,60,43,40,74,55,52} Find the mode of set L, where L= {Numbers…

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

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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: In a group of people, 68 people can speak English, 45 people can speak in Arabic and 19 people can…

A: It is given that 68 people can speak English, 45 people can speak Arabic and 19 people can speak…

Q: {5}⊂{1, 3, 5, 7, 9,...} true or false

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Q: A multiset is similar to a set, but can contain an element more than once. How many multisets can we…

A: You can identify every multiset with an ordered pair of usual sets, call them high and low. If you…

Q: find all poisible tofaloğies on

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Q: S1 = {1,5,25, 125 ,625 ,3125} S2 = {5,11, 17, 23,29,35} S3 = {1,25, 49, 221,169, 289, 3124} S4 =…

A: The solution is given below

Q: How many four-digit numbers can be formed from the digits 0, 1, 2, 3, 4, 5 and 7 if each digit can…

A: i) Since we need a four-digit number, the first digit can never be zero. Thus, the number of ways to…

Q: How many 9-character passwords with only the characters $, #, @, A5, A6,..., A21 are possible if…

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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: A license plate consists of   five symbols on each​ plate, where the first two symbols are letters…

A: Fundamental principle of counting : If an event occur in m ways an corresponding to it another event…

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: user passwords for a certain computer network consist of 6 letters( upper case ) followed by 4…

A: user passwords for a certain computer network consist of 6 letters( upper case ) followed by 4…

Q: For some particular website, the password must start with one of the letters a b or c. Then there…

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

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: There are 10 questions in a final ėxamination for Discrete Mathematics. Each question is assigned at…

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