Answer the following questions for the set S {1, 2, ..., 12}; (Explain how you gotten your answers) (a) How many size-5 subsets does S have? (b) How many size-5 subsets of S contain a 3? (c) How many size-5 subsets of S contain at least one odd number? (d) How many size-5 subsets of S contain exactly one even number?

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A: Given:-                 How many permutations of a set five distinct objects taken three at a time…

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Q: Suppose V is a set and that n(V) = 10. How many subsets of V contain exactly 3 members?

A: Number of ways in which 3 elements of V can be clubbed to form a subset = 10C3…

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Q: Consider all subsets of size four of the set (1,2,3...20) how many of these have a nonempty…

A: Solution :-

Q: A = {k €N:k is odd}

A: Given below the detailed solution

Q: Here is some more practice on calculating the number of elements in a set. 10. Suppose A and B are…

A: Given ,           AC U          BC U          nA=73         nB=56        nU=150To find → nA' &…

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A: ∵ Given that Year Enrollment 2001 5621 2002 5687 2003 5805 2004 5783 2005 5758

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Q: If any subset of size six is chosen from the set S = {-5, -4, -3, -2, -1, 0, 1, 2, 3, 4), then prove…

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Q: If any subset of size six is chosen from the set S = {-5, -4, -3, -2, -1, 0, 1, 2, 3, 4}, then prove…

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Q: Describe the possible inputs of S(n) using words.

A: The possible inputs for S are the numbers on a dice

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: Use the following information to answer question 6. 16 19 The number of elements in the unversal set…

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Q: 1. Suppose in a university, each subject offered to students has a subject code consisting of three…

A: Given that Suppose in a university, each subject offered to students has a subject code consisting…

Q: Suppose A is a set with 6 elements. Answer the following questions:   1. How many subsets of…

A: In a set the order does not matter. So we can use the combination method. 1) We can pick 4 elements…

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Q: Consider all subsets of size four of the set {1, 2, ..., 20}. How many of them have a nonempty…

A: Given: It is given that by considering that all the subsets of size four of the set{1,2,....20} The…

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Q: What are the elements of the following (admittedly peculiar) set: {Alice, {1}}? &#160;

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A: Let us define some events   A:- box 1 is selected B:- box 2 is selected E:- Yellow ball is selected

Q: The following table shows the results of a survey of authors by a fictitious publishing company.…

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Q: Given a set S of size n and A⊆S of size ?k, how many subsets of S contain A?

A: Given : a set S of size n. A⊆S Where the size of the set A is k. To Find : How many subsets of S…

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A: As Dr. S. N. De said "A permutation of a set is defined as an arrangement of its members into a…

Q: (a) How many 4-permutations are there of a set of six objects? (b) How many 2-permutations are there…

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Q: (a) How many 4-permutations are there of a set of five objects? (b) How many 2-permutations are…

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Q: Show that                                n                    n                     (            )…

A: To interpret (hence prove) the given equality of the two binomial coefficients, using set theory

Q: Given the following digits: 2, 3, 5, 6, 7, 9, a. How many 3-digit number combinations can be made…

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Q: Suppose A is a set with 7 elements. Answer the following questions: 1. How many subsets of exactly…

A: Given, A is a set with 7 elements In a set the order doesnot matter so here we use combinations.

Q: How many subsets of size 3 can one find in a set of size 5?

A: Hey, since there are multiple sub parts posted, we will answer the first question. If you want any…

Q: Suppose XX is a set with 144 elements that is partitioned into four subsets: X1, X2, X3, and X4. If…

A: To determine the number of elements in each subset in the partition.

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Q: About the subsets A⊂B⊂CA⊂B⊂C of a universal set UU, except assume that n(A)=5n(A)=5 and…

A: Question concerns the number of different possibilities for the subset B under the given conditions