Ejercicios Combinatoria(2018-2019 ) PDF

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MatemáticaDiscreta.ÁreadeÁlgebra UniversidadedaCoruña

Y

p 0 0 9 X

p≥4 6 X 7

MatemáticaDiscreta.ÁreadeÁlgebra UniversidadedaCoruña

{0, 1, 2} 0 4 16 1

2

MatemáticaDiscreta.ÁreadeÁlgebra UniversidadedaCoruña

0

(x + y)7

(2x + 3y 2 )5

(2x − y)4

xy (x − 2y + 3x−1 )4 w3 x2 yz 2 (2w − x + 3y − 2z)8

(2x − y 2 )5

MatemáticaDiscreta.ÁreadeÁlgebra UniversidadedaCoruña

{1, 2, . . . , 7, 8, 9}

13 · 107 40 > 31 · 1

40 > 12 · 3 40 > 7 · 5

V (6, 5) · V (6, 4) · P (3) = 1555200 C (22, 4) · C (5, 2) · P (6) = 52668000

C(3, 2) · P (6) · P (6) = 1555200

C(10, 3) · C(90, 4) C(100, 7) − C(90, 7)

C (90, 7) + C(90, 6) · C (10, 1)

37 · 36 · 35 · 34 10 · 36 · 35 · 34 V (37, 4) − V (27, 4) V (37, 4) − V (4, 2) · V (35, 2) V (13, 2) · C(4, 3) · C(4, 2) P R(11; 4, 4, 2, 1)

C(13, 2) · C(4, 2) · C(4, 2) · 44

P R(7; 1, 4, 2) · C(8, 4)

P R(7; 1, 4, 2) · V (8, 4)

P R(14; 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1) P R(14; 7, 1, 1, 1, 1, 1, 1, 1) = V (14, 7) = C(14, 7) · 7! 29

C(10, 4) · 26

MatemáticaDiscreta.ÁreadeÁlgebra UniversidadedaCoruña

V R(10, 5) = 105 C(10, 5) = 252

C(10, 4)

P R(10; 2, 3, 5)

V (10, 5) = 30240 C(11, 5)

CR(10, 5) = 2002

P (11) · CR(10, 8) = 11! · C(17, 8) = 11! · 24310 10! = P R(10; 2, 2, 6) P R(4; 2, 2) · CR(5, 6) = 2!2!6! −72

161280, 256

C(14, 5)

C (8, 3) · C (6, 2) C (14, 5) − [C (6, 5) + C (8, 5)] + 0

C (8, 2) + 6 · C (10, 2) C(10, 2) + 2 · 7 · 9 − 2 · 9 − 7 109 109 − 3 · 99 + 3 · 89 − 79

i− x1 + x2 + x3 + x4 + x5 = 20; 1 ≤ xi ≤ 6 %

xi

P7

k k=0 (−1)

  7 · V (20 − k, 7 − k) X k 7 (20 − k)! (−1) = 20! V (20, 7) k

7 k

C(9, 3) · D(6) = 84 · 265

k=0...