The genetic code embodied in the DNA molecule, a code we describe in Section 2.1, consists of strings of symbols, each of which is one of the four letters T, C, A, or G. Find by enumeration the number of different codewords or strings using these letters and having length 3 or less.

  1. A
  2. C
  3. G
  4. T
  5. AA
  6. AC
  7. AG
  8. AT
  9. CA
  10. CC
  11. CG
  12. CT
  13. GA
  14. GC
  15. GG
  16. GT
  17. TA
  18. TC
  19. TG
  20. TT
  21. AAA
  22. AAC
  23. AAG
  24. AAT
  25. ACA
  26. ACC
  27. ACG
  28. ACT
  29. AGA
  30. AGC
  31. AGG
  32. AGT
  33. ATA
  34. ATC
  35. ATG
  36. ATT
  37. CAA
  38. CAC
  39. CAG
  40. CAT
  41. CCA
  42. CCC
  43. CCG
  44. CCT
  45. CGA
  46. CGC
  47. CGG
  48. CGT
  49. CTA
  50. CTC
  51. CTG
  52. CTT
  53. GAA
  54. GAC
  55. GAG
  56. GAT
  57. GCA
  58. GCC
  59. GCG
  60. GCT
  61. GGA
  62. GGC
  63. GGG
  64. GGT
  65. GTA
  66. GTC
  67. GTG
  68. GTT
  69. TAA
  70. TAC
  71. TAG
  72. TAT
  73. TCA
  74. TCC
  75. TCG
  76. TCT
  77. TGA
  78. TGC
  79. TGG
  80. TGT
  81. TTA
  82. TTC
  83. TTG
  84. TTT

for the total of 84 possibilities.

We can verify it by counting:

\[4^1 + 4^2 + 4^3 = 84\]