Show that the number of partitions of n in which odd parts are not repeated but even parts can occur any number of times is equal to the number of partitions of n in which every part is either odd or a multiple of 4.

Q: How many compositions of n are there into k parts of size at least 3?

A: How many compositions of n are there into k parts of size at least 3?

Q: Show that = n. mnZ

A: mZ = set of all integers which are divisible by m mnZ = set of all integers which are divisible by…

Q: 5. How many different wards can be formed with the letters of the word "SUPER' such that the vowels…

A: The word SUPER contain 5 words  The vowels are U and E  Vowels come together so  S,P, R ( UE)  So…

Q: A 6-volume encyclopedia is to be placed on a shelf. How many incorrect arrangements are there?

A: Note- Since you have posted multiple questions, as per our guidelines we are supposed to answer only…

Q: Suppose that in a class, there are n many boys and n many girls. Among these 2n many people, we will…

A: Let A be a set of n elements. To select r objects from a collection of n elements in the set A…

Q: 20

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Q: Faces of a polyhedron are painted into two colors, so that no two faces sharing an edge have the…

A: Consider the provided question, We need to prove that the number of edges of all faces of polyhedron…

Q: Show that the number of integer partitions (of any size) with at most n parts and with largest part…

A: Let Pm,n;N denote the number of partitions of N with at most n parts, each of size at most and with…

Q: find a way to partition N into not two but infinitely many subsets with each subset containing…

A: All the natural numbers can be written in prime factorization form. The natural numbers are the set…

Q: In the laboratory analysis of samples from a chemical process, seven samples from the process are…

A: Answer:----.            Date:----8/10/2021 1)  Number of different sequences of process and control…

Q: Show that for any positive integer n, with n not equal to 2, there exists a partition of n that is…

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Q: Prove that the number of partitions of n into at most k parts is equal to that of partitions of n +…

A: given , number of partitions of n into k parts  we have to prove that , partitions of number n + k…

Q: Is there a formula to find the number of partitions in a set with n-elements?

A: Bell numbers, Bn, gives the number of partitions of a set with n elements It counts the number of…

Q: (3) Find the formula for the number of ways for putting n identical balls into k distinct boxes so…

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Q: Prove that the number of partitions of n into parts of size 1 and 2 is equal to the number of…

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Q: Compute the sum of all integers between 60 and 150 that are exactly divisible by 8.

A: Consider the given range of number 60 to 150

Q: Show that for all n:  ceil(n) = -floor(-n)

A: In the given question we have to prove that ceil(n)=-floor(-n) That is…

Q: In how many ways can 25 identical doughnuts can be distributed to 4 police officers so that each…

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Q: How many elements are there in the greatest conjugacy class of 5 ?S

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Q: Find the number of permutations without replacement that can be created by drawing 5 balls from a…

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Q: Compute the sum of all integers between 40 and 100 that are exactly divisible by 3.

A: Compute the sum of all integers between 40 and 100 that are exactly divisible by 3.

Q: Suppose 82 jelly beans are distributed among 9 kids, with some kids possibly getting none. Fill in…

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Q: Use Fermat's Theorem to show that n 13 - n is divisible by 2730 for all n.

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Q: Show that the generating function for the number of self-conjugate partitions of n is (1– x²)(1 –…

A: To Show : Show that the generating function for the number of self-conjugate partitions of n is  ∑k…

Q: Find the ordinary generating function for the number of partitions of n in which no part occurs more…

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Q: In the laboratory analysis of samples from a chemical process, seven samples from the process are…

A: Given : 7 samples are process 1 control sample analyzed twice Hence , total items  = 9   a) If we…

Q: In how many ways can 25 identical donuts be distributedto four police officers so that each officer…

A:

Q: With 100 candidates, find the number of permutations that can be made if 10 beauty queens are…

A: Given total number of candidates, n                 n = 100  Number of beauty queens that are to be…

Q: Assume that n > 2 and x E A is a fixed element. How many unordered selections without repeats of k…

A: N>2, X is the element A is a fixed element  How many unordered selections withouts repeats of  k…

Q: It was reported in 2007 that there were 7,546,000 people age 16 or older who had a​ "go outside…

A: It is an important part of statistics. It is widely used.

Q: find the sum of all even intergers less than 1000 that are exactly divisible by 7

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Q: 4. In how many ways can a committee of 5 memebers be chosen from a group of 10 memebrs?

A: Given that, The number of members in the committee is 5. And the total number of members is 10. So,…

Q: partition of Z into four subsets.

A:

Q: Find the number of self-conjugate partitions of 17 and list all of them.

A: There are 3 odd distinct partitions in 17. 13+3+111+5+19+5+3

Q: Discuss the important characteristic that a counting problem has to have in order to classify it as…

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Q: how many positive intergers less than 1150 are multiples of 8, 5, 3. using the principles of…

A: Floor Function: The floor function , also called the greatest integer function or integer value,…

Q: It is true that the division algorithm does not hold for Z[x]. Provide an example to show why.

A: It is given that the division algorithm does not hold for Z[x] Example Let us take a subset S of…

Q: Use generating functions to find the number of ways tochoose a dozen bagels from three…

A: Consider the provided question, Each variety is present at least 2 times in the dozen bagels, the…

Q: In how many ways can you partition a set of 8 elements into 3 subsets (compute S8.3)?

A: To find - In how many ways can you partition a set of 8 elements into 3 subsets compute S8, 3 ?…

Q: Suppose that there are n = 2k teams in an eliminationtournament, where there are n∕2 games in the…

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Q: Prove that the number of partitions of n into exactly k parts is equal to the number of partitions…

A: Each partitioning can be drawn out in the following manner: draw a column of xs that represents the…

Q: 5. Suppose we have an enumeration of A ao, a1, A2, ·.. (1) without repetitions (i.e., all the a; are…

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Q: How many possible of size n=4 can be drawn from a population of size 15?

A: Population size z N= 15 And we want to draw n=4 size of samples.  There are NPn ways to draw the…

Q: How many different 5-block (5-part) partitions can be made of the set A = {1,2,3, 4, 5, 6}.

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Q: How many partitions does the set [10] = {1,2,3,,10} have, in which each part has two elements. How…

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Q: Calculate the number of permutations of {1,2,3,4,5,6} with three cycles (a) by using the recursion…

A: We need to calculate the number of permutations of 1, 2, 3, 4, 5, 6 with three cycles. For (a),…

Q: Which fraction have decimal representation that are not finite and repeat infinitely? 1 /2 ,1/3,…

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Q: Find the number of ways 66 identical coins can be separated into three nonempty piles so that there…

A: GivenTotal number of identical coins =66Total number of piles =3 Each pile is on empty and the…

Q: circular convolution of sequences

A: Circular convolution using circular convolution: x1(n) = {a, b, c, d} and  x2 (n) = {4, 3, 2, 2}…