Use inclusion-exclusion to find the number of ways to arrange the six numbers 1, 2, 3, 4, 5, 6 such that either 1 is immediately followed by 2, or 3 is immediately followed by 4, or 5 is immediately followed by 6

Q: How many distinct proper subsets are there of the set N = {6, 44, 62, 14, 40, 51, 23}?

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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…

Q: Prove that any positive integer greater than or equal to 8 can be written as a sum of 3's and 5's.…

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Q: How many distinct proper subsets are there of the set N = {9, 46, 69, 18}?

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Q: How many ways are there to form a subset of [n] of size k with the property that each selected…

A: Given n=8 k=3 4 ways 1,4,7,1,4,8,1,5,8 and 2,5,8 Find How many ways are there to form a subset of n…

Q: Suppose that the number of subsets with k elements, made out of a set of n elements is called by the…

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Q: Let A be the set of five-digit numbers where only the digits 1, 2 and 3 are included. For example…

A: Given that A is the set of five-digit numbers where only the digits 1, 2 and 3 are included.  So,…

Q: Use the definition of an r-permutation, or the product rule to de number of trifectas possible in a…

A: Given: To explain the given statement as follows:

Q: Let $n$ be a positive integer. Among C(2n,0),C(2n,1),..., C(2n,2n), C(2n,n) is the largest. True…

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Q: A(n) _______ is an ordered arrangement ofr objects chosen from n objects.

A: We fill the blank space as

Q: Use the principle of inclusion-exclusion to determine the number of arrangements of length n, n > 3,…

A: Explanation use the principle of inclusion -exclusion to determine the number of arrangement of…

Q: Determine the number of permutations of the set {1 ,2 ,..., 14} in which exactly 7 integers are in…

A: Solution-:

Q: Suppose a set of 8 numbers are selected from the set: {1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13;…

A: It is given that 8 numbers are selected from the set 1,2,3,4,5,6,7,8,9,10,11,12,13,14.

Q: Show that the set {2/3,1/3,2/9,1/6...} is countable

A: Given set of numbers{2/3, 1/3, 2/9, 1/6...}. Here, this set of rational numbers will be proved as…

Q: Given 10 numbers a1, a2,.… , a10, from the set S natural numbers S = {1,2,3, ., 100} . Prove that…

A: Consider the set S=1, 2, 3, …, 100. Let a1, a2, …, a10 be 10 numbers from the set S. Take the set…

Q: How many triples of integers from 2 through 16 can be formed in which the integers are in increasing…

A: Any triple of integers (i, j, k) with 2 ≤ i ≤ j ≤ k ≤ 16 can berepresented as a string of 15 – 1…

Q: Assume that product codes are formed from the letters Q, X, W, T, S, Z, and Y, and consist of 6 not…

A: 1) There are total 7 letters, such that, Q, X, W, T, S, Z and Y.

Q: 3.55. a) How many three-digit numbers with different digits are there formed by digits belonging to…

A: As per the honor code, We’ll answer the first question since the exact one wasn’t specified. Please…

Q: In how many distinct ways can the digits in the number 1,238,229,168 be arranged?

A: We have to find in how many ways the number  1,238,229,168 can be arranged.

Q: How many different ways can you arrange 2 letters from a set of 3 letters {T, S, U} such that…

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Q: Assume that product codes are formed from the letters X, T, and R, and consist of 6 not necessarily…

A: Given,  Product codes are formed from the letters X, T, and R, and consist of 6 not necessarily…

Q: 4. Show that if n is a positive integer, then Σ {a₁,...,ak}{1,2,...,n} (Here the sum is over all…

A: Given, If n is a positive integer, then we have to show that ∑a1,.....ak⊆1,2,....,n 1a1a2....ak=n

Q: Number theory

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Q: Determine whether the selection is a permutation, a combination, or neither. Mary baked 3 pies: 1…

A: The answer is permutation.

Q: ct proper subsets are there of the set N = {3, 43}?

A: The number of elements in the set are 2 ( which are 3, 43)

Q: Let [A1, A2. [B1, B2, C1, C2 be 3 married couples who attended a concert in Windhoek. a) In how many…

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Q: Use pigeonhole principle 1. How many numbers must be selected from the set {1, 3, 5, 7, 9, 11, 13,…

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Q: Find the number of permutations x1, x2, x3, x4, x5,  of numbers 1, 2, 3, 4, 5 such that the sum of…

A: A number is divisible by 3 when one of the factors of the number is 3. Thus the sum…

Q: { n ∣ n ∈ N and 405 < n ≤ 437} H has --------  subsets. H has--------  proper subse

A: It is given that ,  H=n|n ∈N and 405 &lt; n ≤437we have to find , H has ................. subsets.H…

Q: A product code consists of a string of 4 different letters selected from the set {S,T,U,V,W,X}. How…

A: The number of ways to arrange r objects selected from n distinct objects is given by the permutation…

Q: How many distinct proper subsets are there of the set N = {9, 41, 68, 17, 33, 54}?

A: Number of the proper set = 2n -1

Q: compute the sum of all integers between 60 and 110 that are exactly divisible by 7

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Q: 6. (a) Show, using the pigeonhole principle, that in any set of 5 integers, at least two have the…

A: (a) Show that any set of 5 integers at least have two the same remainder when it is divided by 4…

Q: Prove that a selection of 7 numbers from the set {1, 2, . . . , 11} contains numbers m and n such…

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Q: [Q1] From the letters {A, B, C, D, E, F, G}, how many: (a) 3-distinct-letters co can be generated?…

A: Given: There are 7 letters A, B, C, D, E, F, G

Q: How many four​-digit numbers may be formed using elements from the set {1, 2, 3, 4, 5, 6, 7} if no…

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Q: How many subsets are there of the set (1, 2, 3, 4, 5, 6, 7, 8, 9, 10} which contain at least three…

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Q: How many distinct proper subsets are there of the set N = {7, 44, 68, 19, 32, 54, 25}?

A: This question is about set theory

Q: Assume that product codes are formed from the letters V, T, X, R, S, and Y, and consist of 6 not…

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Q: 13. Determine the number of permutations of {1,2, . , 9} in which at least one odd integer is in its…

A: Solution : There are total 9 numbers from which five numbers  are odd (1, 3, 5, 7, 9) and four are…

Q: How many words can be formed by permutation of the letters of the word DEPRESSION such that each…

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Q: How many subsets are there of the set N = {1, 44, 65, 11, 39, 53, 26}?

A: Given,          The set is N=1, 44, 65, 11, 39, 53, 26We know that,          The number of subsets…

Q: MK18. Show that in any set of 9 integers chosen from the set {2,3, 4, ... , 21, 22}, there are at…

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Q: Using the inclusion-exclusion principle, find the number of integers from a set of 1-100 that are…

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Q: How many 5-tuples (x1, x2, x3, x4, X5) of positive integers from 1 to n are there? How many 5-tuples…

A: Since you have asked multiple questions, we will solve the Question Q1 (a) and (b) and (c) for you.…

Q: Find the number of subsets of the set (1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11} having 4 elements. * 340…

A: Find the number of subsets of the set 1,2,3,4,5,6,7,8,9,10,11 having 4 elements

Q: many permutations can be formed with two types of objects with n objects of type 1 and n^2 objects…

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Q: Let A be the set of five-digit numbers where only the digits 1, 2 and 3 are included. For example…

A:

Q: Use mathematical induction to prove that for every integer n >=2, if a set S has n elements, then…

A: We have to prove that The given statement is for every integer n ≥ 2, if a set S has n elements.

Q: We are making 5-letter words from the set of letters a, b, c, d, e, f..., in such a way that we have…

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

Counting Principles

In statistics, the counting principle can be said to be the concept in which the quantity of an item is determined. There can be a single item, or a group of items, or items that are related to each other. In every possible set of items, the quantity of the possible item groups or their sorting measures can be determined with counting principles.