EXERCISE 4.2.9. Let P be the set of people in a group, with |P| = p. Let C be a set of clubsformed by the people in this group, with |C| = c. Suppose that each club contains exactly gpeople, and each person is in exactly j clubs. Use two different ways to count the number of pairs (b, h) € P x C such that person b is in club h, and deduce a combinatorial identity. in Club h. and deduce a combinational identity,{ (b.h) = PxCLet I = SC bin) (PxC (b is in h)ThenIC PXCNI PM₂ I-SCPersen bis in clubb'sbin) b(bib) h шишу дUse different ways of countingthe number of pairsThis section is read-containin{(b, h) € PxC person bisclub hSolutionLetinThenI = {(A,^) ( P. C | beit).we haveIc PxCJpairs (bh)such that belKWe can define mapsStall pairsT₁₂: I Cin7₁: IPprojection(b, h) b (forget the 27andCoordinate(b) h"2ndprojection(forget the 1stwordinate)

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

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) € P x C such that person b is in club h, and deduce a combinatorial identity.

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) € P x C such that person b is in club h, and deduce a combinatorial identity.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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