SOLUTION: In a certain city, there are four streets going north-south and seven streets going east-west. How many street paths start at the southwest corner of the city, end at the northeast

Suppose the grid of streets is like this:



To get from the green circle to the red circle the shortest
way, we must move through 9 blocks.  We must pick 3 of those
blocks the go east and the rest north.  For example, one way
we can go is ENNENNNEN.  That would be the green path below:

 

So of the 9 blocks, we must pick 3 blocks to turn east (right),
and the rest we will go north (up) so the answer is 

9C3 = 84 

ways to go 9 blocks from the green circle to the red circle.

FYI, here is a computer-generated list of all 84 ways:

 1. EEENNNNNN
 2. EENENNNNN
 3. EENNENNNN
 4. EENNNENNN
 5. EENNNNENN
 6. EENNNNNEN
 7. EENNNNNNE
 8. ENEENNNNN
 9. ENENENNNN
10. ENENNENNN
11. ENENNNENN
12. ENENNNNEN
13. ENENNNNNE
14. ENNEENNNN
15. ENNENENNN
16. ENNENNENN
17. ENNENNNEN
18. ENNENNNNE
19. ENNNEENNN
20. ENNNENENN
21. ENNNENNEN
22. ENNNENNNE
23. ENNNNEENN
24. ENNNNENEN
25. ENNNNENNE
26. ENNNNNEEN
27. ENNNNNENE
28. ENNNNNNEE
29. NEEENNNNN
30. NEENENNNN
31. NEENNENNN
32. NEENNNENN
33. NEENNNNEN
34. NEENNNNNE
35. NENEENNNN
36. NENENENNN
37. NENENNENN
38. NENENNNEN
39. NENENNNNE
40. NENNEENNN
41. NENNENENN
42. NENNENNEN
43. NENNENNNE
44. NENNNEENN
45. NENNNENEN
46. NENNNENNE
47. NENNNNEEN
48. NENNNNENE
49. NENNNNNEE
50. NNEEENNNN
51. NNEENENNN
52. NNEENNENN
53. NNEENNNEN
54. NNEENNNNE
55. NNENEENNN
56. NNENENENN
57. NNENENNEN
58. NNENENNNE
59. NNENNEENN
60. NNENNENEN
61. NNENNENNE
62. NNENNNEEN
63. NNENNNENE
64. NNENNNNEE
65. NNNEEENNN
66. NNNEENENN
67. NNNEENNEN
68. NNNEENNNE
69. NNNENEENN
70. NNNENENEN
71. NNNENENNE
72. NNNENNEEN
73. NNNENNENE
74. NNNENNNEE
75. NNNNEEENN
76. NNNNEENEN
77. NNNNEENNE
78. NNNNENEEN
79. NNNNENENE
80. NNNNENNEE
81. NNNNNEEEN
82. NNNNNEENE
83. NNNNNENEE
84. NNNNNNEEE

Edwin