(a) How many three digit numbers can be formed from the digits 0, 1, 2, 3, 4, 5, 6 and 7 such that the numbers are divisible by 5 and none of the digits is repeated?

Q: 4. How many subsets are there of {1, 2, 3, 4, 5}? How many contain at least three elements? How many…

A: Given set is S=1,2,3,4,5 Since we know that, if a set contains n elements, then total number of…

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Q: If repetition of digits is not​ allowed, how many four​-digit numbers can be formed using the…

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Q: . How many 3-digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 9, which are divisible by…

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Q: How many strings of 12 ternary digits (0, 1, or 2) are there that contain exactly three 0s, five 1s,…

A: Total number of digits are 12 Given there are three 0's , five 1's and four 2's

Q: 3. Show that the weighted arithmetic mean of first n natural numbers whose weights are equal to the…

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Q: How many ways can the letters of the word MAILBOX be arranged in a row so that  M and A Not…

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Q: Show that an integer N is divisible by 9 if and only if the sum of its digits is divisible by 9

A: Let a=anan-1...a3a2a1 be an integer and S be the sum of the digits. Consider a,…

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

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Q: 10. How many numbers greater than 500 can be formed from the digits 2, 3, 5, 8, and 9 using each…

A: Given Data : The given numbers are : 2,3,5,8 & 9 To Find : Total numbers greater than 500 formed…

Q: 13. How many 3-digit numbers can be formed using digits from {1,2,3,4,5} if repeated digits are not…

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Q: (a) Show that if seven integers are selected from the first 10 positive integers, there must be at…

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Q: 1. How many 3 or 4 digit even numbers greater than 700 can be formed by: a. Using the digits 0-9.…

A: Let there are three chairs A, B and C in one side of a table. The different ways in which these…

Q: 1) There are 480480 people in attendance for the conference. If every person shook hands with every…

A: Hello. Since your question has multiple parts, we will solve the first three parts for you. If you…

Q: 5. Prove that the sum of the first n natural numbers is equal to n(n+ 1)/2, and deduce that the sum…

A: Sum of n number is given by

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Q: From the digits 1,2,3,4,5,7 and8 a) How many numbers of four different digits each can be formed? b)…

A: Given  The digits 1,2,3,4,5,7and 8  a). How many numbers of four digits each can be formed. b). How…

Q: Consider five-digit numbers  = a1 a2 a3 a4 a5, with each digit from the set {1, 2, 3, 4}. a. How…

A: Solution is given as below:

Q: 4. How many 5 digit numbers can be formed if a) the digits 2-8 are available and there must be at…

A: 4. It is required to form 5 digit numbers under two different sets of conditions.

Q: ) A group of people born within the week. At least 6 people born on the same day. At least how many…

A: As per the guidelines we are allowed to solve maximum of 1 question If you need help with other…

Q: A) How many integers, greater than or equal to10000 but less than or equal to 39999, can be formed…

A: Note :- We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: 1- The total number of positive integers that can be formed from the digits 1,2,3 and 4 if no digit…

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Q: 12 11 10 8. 2 (4, 1) -12-11-10-9-8 -7 -6 -5 -4 -3/2 -1 1 2 3 4 5 7 8 9 10 11 12 -2 8-4). -5 -6 -7 -8…

A: This question is related to circle . We will solve this question by using standard centre- radius…

Q: Prove a number is divisible by 3 if and only if the sum of its digits is divisible by 3.

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Q: 2. A group contains k men and k women, where k is a positive integer. How many ways are there to…

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Q: 1)How many integers between 1000 and 2000 are divisible by at least one of the integers 3, 5 and 7?

A: Introduction: In mathematics, integers are the sum of positive and negative numbers. Integers are…

Q: How many 5-digit license plate numbers can we generate from the numbers, 0, 1, 2, 3, and 4 if it…

A: As per the company policy i can answer only first question for you,more than that leads me towards…

Q: Show that the weighted arithmetic mean of first 'n' natural numbers whose weight are equal to the…

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Q: An n×n magic square is a square array of numbers (n > 1) such that the sum of every row, of every…

A: Given a n×n magic square

Q: Prove that if the sum of the digits is subtracted from a natural number, then the result is…

A: let us assume the number to be three digit number xyz therefore, xyz=100x+10y+z sum of digits will…

Q: VI How many combinations are there if 11 distinct things taking 4 at a time?

A: Hey there! As per our company policy we can answer only 1 ques at a time. Please make a new request…

Q: n how many distinct ways can the digits in the number 1,243,520,326 be arranged? (If there are any…

A: Given number 1,243,520,326 Total number of digits=10 Number of 1's=1 Number of 2's=3 Number of 3's=2…

Q: 9. Consider a number with 8 digits but using only digits 1, 2, 3 and 4. a) How many numbers can we…

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Q: How many 5-digit numbers can be made from the digits 1 to 9 if: a) Repetition of digits is allowed?…

A: Here AS PER POLICY I HAVE CALCULATED FIRST 3 SUBPART ONLY

Q: How many five-digit numbers are there for which each digit is either equal to both adjacent ones, or…

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Q: set of two - digit numbers obtained from the digits 1

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Q: How many ways are there to permute the elements of the multiset {1,1,2,2,3,4,5,6} so the first and…

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Q: 1- The total number of positive integers that can be formed from the digits 1,2,3 and 4 if no digit…

A: NOTE- AS PER POLICY I  HAVE CALCULATED FIRST MAIN QUESTION ONLY. Here Given 4 digits 1,2,3,4

Q: 3) Among a group of seven (not necessarily consecutive) integers, how many must be divided by 5 to…

A: This is a problem related to divination rule of the mathematics. Based on the general concept we…

Q: How many 5-digit numbers can be formed using the digits 2, 3, 4, 5, and 6 without repetition? With…

A: To find how many   5 digit number  can be formed using  2,3,4,5 and 6 without  repetition and then…

Q: (a) How many permutations of (10] are there that EITHER alternate even and odd numbers or have even…

A: Let consider the permutations of 10 as the ordering of  the elements of 10 rather than as an…

Q: In how many different ways can the letters of the word “CORPORATION” be arranged so that the vowels…

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: How Many perMutations of the digits 0, I, 2, 3. 4, 5, 6, 7, 8, 9 are there in which the digitss…

A: The permutation represents the number of ways something can be arranged. In permutations or…

Q: 74. P is a natural number of at least 6 digits and its left- most digit is 7. When this leftmost…

A: Introductions :

Q: In how many ways can a person select seven party guests from 12 women  if he is to avoid having a…

A: Here we will use the concept of Combination

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Q: 8. Find the number of different salads consisting of one or more of these vegetables – Tomatoes,…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: -Each student at State University has a student ID number consisting of five digits (the first digit…

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Q: A man finished a job in 5 days. On the first day, he finished 1/m of the job. On the second day, he…

A: GIVEN THAT JOB FINISHED = 5 DAYS