HOMEWORK SOLUTIONS for Chapters 5 & 6

NOTE: Solutions of ODD-numbered problems are in back of text.

Homework Assignment #6
Section 5.1 6. n x (n-1); 12. 5^2 x 26^2, 26^2 x 21^2; 16. 16a) 36^2, b) 1/36, (1^2 + 2^2 + 3^2 + 4^2 + 5^2 + 6^2 + 5^2 + 4^2 + 3^2 + 2^2 + 1^2)/36^2 = 146/1296, d) 1/2[1 - 146/1296]; 20. (11^2+10^2)/21^2; 26. 4x3x8x8/10^4; 36. 2 x 85/(100x99).
Section 5.2: 4. 8!, 2 x 4!^2; 8. C(13,5), C(8,3) x C(5,2)/C(13,5); 16 b)13x48/C(52,5), c) C(13,2) x C(4,2)^2 x 44/C(52,5), d) 13 x C(4,3) x 12 x C(4,2)/C(52,5), 38. 11!/4! - 10!/4!;

Homework Assignment #7
Section 5.1: 24. 10^8; 30. see Supplement at end of Chap. 32. (3 + 3 + 1)/80;
Section 5.2: 32. C(13,2)xC(4,2)^3x44; 34. C(5,2)xC(5,3) + C(5,3)xC(5,2) + C(5,4)xC(5,1) + C(5,5); 51. See Supplement.
Section 5.3: 2. 11!/4!4!2!1!; 4. 3 x 6!/3!3! + 6!/2!3 + 3! x (6!/3!2!1!); 12. sum over k=0 to 3 of C(3,k) x C((10-k)+3-1,(10-k)).
Section 5.4: 2a) 4^16, b) C(4,2)x16!/6!6!2!2!, c) 16!/4!^4; 10. C((21-4) + 6 - 1, (21-4)) x 21! x 5!; 12a) C(28+5-1,28); 27. see Supplement.

Homework Assignment #8
Section 5.2: 22. 13!^4/(52!/4!^13; 52. C(k -1,2) x (20 - k)/C(20,4);.
Section 5.3: 22a) 3x10!/4!3!2!1!, b) C(10,5)xC(4,2)x5!/2!.
Section 5.4:28. See Supplement; 48. 8[(1+4-1,1)x5!/2! .
Section 6.1: 2b) (x+x^2+... x^4)^3, c) (x^2 + x^4 + x^6)(x^3 + x^5)(x+2 + x^3 . . + x^6)^2; 4b) (x^3 + . . + x^6)^4, c) (x + x^2 + x^3 + . . .)^7; 6. (1 + x + x^2 + . . . )^5; 10. (1+x)^u (1 + x + x^2)^v (1 + x + x^2 + x^3)^w.