EXERCISE 4.2.9. Let P be the set of people in a group, with |P| = p. Let C be a set of clubs formed by the people in this group, with |C| = c. Suppose that each club contains exactly g people, and each person is in exactly j clubs. Use two different ways to count the number of pairs (b, h) E P x C such that person b is in club h, and deduce a combinatorial identity. hin

Q: In this question and subsequently, let d₁, d2, ..., d5 denote the first five digits of your exam…

A: Given : Let d1, d2, d3, d4, d5 denote the first five digit of exam number and X denote the set…

Q: 2. Let A = {r|x is older than 25}, B = {y|y_is older than 50}, C = {z |z is between 20 and 30}. Draw…

A: The question is related to sets. The solution is explained below.

Q: 6. Let set E = {0,2, 4,6, 8,10} , F = {2,3,5,7,11} : a. Find P(E and F) b. Find P(E or P)

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Q: (d) List all outcomes in the event D that exactly two vehicles go in the same direction. D = (e)…

A: See the handwritten solution

Q: EXERCISE 4.2.9. Let P be the set of people in a group, with |P| = p. Let C be a set of clubs formed…

A: Given P is the set of people in a group, with P=p. C is the set of clubs formed by the people in…

Q: Suppose n(A) = 16, n(B) = 29, and n(A U B) = 36. Use a Venn diagram to find n(An B). A B

A: We have, nA = 16nB = 29nA∪B = 36 To determine: The value of nA∩B. Formula Used: nA∪B = nA+nB-nA∩B.

Q: Illustrate the key ideas in the proof of Hall's Matching Theorem.

A: A bipartite graph is a graph G = (V, E) whose vertex set V may be partitioned into two disjoint set…

Q: 6. Let X and Y be subsets of {a,b}. Write the relation where X is related to Y if |X| = |Y| as a set…

A: Let  A={a ,b }  Cardinality of A=2 so the cardinality of power set is 2^2 =4 Now power set of A is…

Q: C. Draw a Venn Diagram showing the number of students in each of the eight sections of the Venn…

A: Note: as per guidelines we support only three subparts of the questions.kindly repost next question…

Q: Use a Venn diagram to answer. If n(A) = 8, n(B)= 10 and n(A N B) = 3, what is n(AU B)? %3D n(A U B)…

A: Answer - Given,   n(A)  = 20,  n(B)  = 24,  and  n( A∩B )  = 3             Find n( A U B )   = ?

Q: How many elements of order 5 are in S7?

A:

Q: Let S = (a, b, c, d, e, f with P(b) = 0.16, P(c) = 0.12, P(d) = 0.29, P(e) = 0.22, and P(f) = 0.11.…

A: Given S = { a, b, c, d , e , f } P( b ) = 0.16P( c ) = 0.12 P( d ) = 0.29 P( e ) = 0.22 P( f ) =…

Q: jim has precisely 150 followers. and, all 150 people who follow jim have precisely 150 followers. In…

A: Given that Jim has followers 150 in number. Also, each follower of Jim follows Jim and 149 others…

Q: {-5, –3, –1, 1, 3, 5}, Let A 3D {-5, —-4, —3, —2, —1,0, 1, 2, 3, 4, 5}, В D = {1,2, 3, 4}, E =…

A:

Q: Use the given information to fill in the number of elements for each region in the Venn diagram. W A…

A:

Q: Let U = {7, 8, 9, 10, 11, 12, 13}, A = {7, 8, 9, 10}, B = {7, 8, 11, 12}, and C = {9, 11, 13}. List…

A: We have to find given sample space.

Q: 2. Let f and g be any permutations. Show that the order of h = fgf- is the same as the order of g.

A: Here f and g are tow permutations  and we are given that h=fgf-1. We have to show that both f and g…

Q: Consider the monthly salary of all 5 employees of a company: Salary={20,30,22,20,16} Choose any…

A: Given that The monthly salary of all 5 employees of a company. Salary={20,30,22,20,16}

Q: 4. Let A

A: Given,                A=1, 2, a, b, ϕ

Q: Consider the following two sets:   C = {–10, –8, –6, –4, –2, 0, 2, 4, 6, 8, 10} B = {–9, –6, –3,…

A:

Q: jim has precisely 150 followers. and, all 150 people who follow jim have precisely 150 followers. In…

A: Given that Jim has 150 followers and a follower of Jim follows Jim and 149 others. Let the set S is…

Q: Let S = {a, b, c, d, e, f} with P(b) = 0.21, P(c) = 0.25, P(d) = 0.2, P(e) = 0.1, and P(f) = 0.11.…

A:

Q: 2. Let S = {0, 1, 2, 3, 4} and T = {0, 2, 4). (a) How many ordered pairs are in S × T? T × S? (b)…

A: 12. Given that,                    S=0, 1, 2, 3, 4  & T=0, 2, 4.

Q: 4. Let M = {Civic, Corolla, Altima} and S = {Coupe, Sedan} List the elements of M x S.

A: Let M=Civic, Corolla, Altima and S=Coupe, Sedan

Q: P29.10 Determine the number of permutations of size 3 that can be made from the set {1, 2, 3, 4, 5,…

A: