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The Blues' 2-1 fourth round qualifying win sends Rob Elliot's side into the hat as clubs from Leagues One and Two now join the competition.
The draw will be live on TNT Sports on Monday with the show starting at 6.30pm and the draw starting about five minutes later.
The show will be hosted by Matt Smith and the draw will be made by Martin Keown and Fara Williams. It will be available to watch on TNT Sports 1, HBO Max, and on the TNT Sports YouTube channel.
With the draw no longer regionalised, Carlisle's potential opponents range from the upper reaches of League One to the ninth tier.
Minnows still in the competition include ninth-tier Tadley Calleva, the Combined Counties League Premier Division South outfit who earned a replay against National League club Aldershot Town.
Eighth-tier AFC Rushden & Diamonds from the Northern Premier League Midlands Division are in the draw after their 2-1 win over Morecambe, with eighth-tier Stafford Rangers also in the hat after their draw with Gateshead.
Potential opponents from the seventh-tier include Guiseley, Wimborne Town, Berkhamstead, Sholing and Plymouth Parkway, with several other seventh-tier sides also in the draw after earning replays.
Wimborne, whose general manager is Brunton Park hero Jimmy Glass, got past Chelmsford City, while fellow Southern League Premier South side Berkhamsted shocked Southend United at Roots Hall.
The highest-placed team in the draw will be League One leaders Bradford City.
There are several potential long away days in the draw, meanwhile, including the likes of Plymouth Argyle, Plymouth Parkway and Dover Athletic.
FA CUP FIRST ROUND DRAW BALL NUMBERS
1. Accrington Stanley
2. AFC Wimbledon
3. Barnet
4. Barnsley
5. Blackpool
6. Bradford City
7. Bristol Rovers
8. Bromley
9. Burton Albion
10. Cambridge United
11. Cheltenham Town
12. Chesterfield
13. Colchester United
14. Crawley Town
15. Crewe Alexandra
16. Doncaster Rovers
17. Exeter City
18. Fleetwood Town
19. Gillingham
20. Grimsby Town
21. Huddersfield Town
22. Leicester City
23. Leyton Orient
24. Luton Town
25. Mansfield Town
26. Milton Keynes Dons
27. Newport County
28. Northampton Town
29. Notts County
30. Oldham Athletic
31. Oxford United
32. Peterborough United
33. Plymouth Argyle
34. Port Vale
35. Reading
36. Rochdale
37. Rotherham United
38. Salford City
39. Sheffield Wednesday
40. Shrewsbury Town
41. Stevenage
42. Stockport County
43. Swindon Town
44. Tranmere Rovers
45. Walsall
46. Wigan Athletic
47. Wycombe Wanderers
48. York City
49. Harborough Town
50. Chorley or Worcester City
51. Gateshead or Stafford Rangers
52. FC Halifax Town
53. Guiseley
54. Barrow or Gloucester City
55. Marine
56. Scunthorpe United
57. Macclesfield or Anstey Nomads
58. Altrincham or FC United of Manchester
59. Bury or Harrogate Town
60. Spalding United or Alvechurch
61. AFC Rushden & Diamonds
62. Kidderminster Harriers
63. Carlisle United
64. AFC Fylde
65. Salisbury
66. Sutton United
67. Chesham United or Forest Green Rovers
68. Leatherhead or Yeovil Town
69. Bedford Town or Cray Wanderers
70. Hornchurch
71. Aldershot Town or Tadley Calleva
72. Oxford City
73. Wimborne Town
74. Wealdstone
75. Boreham Wood
76. Eastleigh
77. Berkhamsted
78. Sholing
79. Plymouth Parkway
80. Dover Athletic