SOLUTION: How many 4 letter words (doesn’t matter if they are nonsense) can be made from the letters AABBCD?

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Question 775270: How many 4 letter words (doesn’t matter if they are nonsense) can be made from the letters AABBCD?
Answer by Edwin McCravy(20055)   (Show Source): You can put this solution on YOUR website!
AABBCD
We first work it as if the A's were distinguishable, as if it were

AaBbCD

Then there would be 6! = 720 ways

However, the A and a could be arranged in each arrangement
in 2! ways, and the B and the b could be arranged in 2! ways,
and we wouldn't be able to tell the difference, so we must
divide twice by 2!.

Answer  =  =  = 180 ways.

Here are all 180 ways:

1. AABBCD  2. AABBDC  3. AABCBD  4. AABCDB  5. AABDBC  6. AABDCB  7. AACBBD  8. AACBDB  9. AACDBB  10.  AADBBC
11. AADBCB  12. AADCBB  13. ABABCD  14. ABABDC  15. ABACBD  16. ABACDB  17. ABADBC  18. ABADCB  19. ABBACD  20.  ABBADC
21. ABBCAD  22. ABBCDA  23. ABBDAC  24. ABBDCA  25. ABCABD  26. ABCADB  27. ABCBAD  28. ABCBDA  29. ABCDAB  30.  ABCDBA
31. ABDABC  32. ABDACB  33. ABDBAC  34. ABDBCA  35. ABDCAB  36. ABDCBA  37. ACABBD  38. ACABDB  39. ACADBB  40.  ACBABD
41. ACBADB  42. ACBBAD  43. ACBBDA  44. ACBDAB  45. ACBDBA  46. ACDABB  47. ACDBAB  48. ACDBBA  49. ADABBC  50.  ADABCB
51. ADACBB  52. ADBABC  53. ADBACB  54. ADBBAC  55. ADBBCA  56. ADBCAB  57. ADBCBA  58. ADCABB  59. ADCBAB  60.  ADCBBA
61. BAABCD  62. BAABDC  63. BAACBD  64. BAACDB  65. BAADBC  66. BAADCB  67. BABACD  68. BABADC  69. BABCAD  70.  BABCDA
71. BABDAC  72. BABDCA  73. BACABD  74. BACADB  75. BACBAD  76. BACBDA  77. BACDAB  78. BACDBA  79. BADABC  80.  BADACB
81. BADBAC  82. BADBCA  83. BADCAB  84. BADCBA  85. BBAACD  86. BBAADC  87. BBACAD  88. BBACDA  89. BBADAC  90.  BBADCA
91. BBCAAD  92. BBCADA  93. BBCDAA  94. BBDAAC  95. BBDACA  96. BBDCAA  97. BCAABD  98. BCAADB  99. BCABAD  100.  BCABDA
101. BCADAB  102. BCADBA  103. BCBAAD  104. BCBADA  105. BCBDAA  106. BCDAAB  107. BCDABA  108. BCDBAA  109. BDAABC  110.  BDAACB
111. BDABAC  112. BDABCA  113. BDACAB  114. BDACBA  115. BDBAAC  116. BDBACA  117. BDBCAA  118. BDCAAB  119. BDCABA  120.  BDCBAA
121. CAABBD  122. CAABDB  123. CAADBB  124. CABABD  125. CABADB  126. CABBAD  127. CABBDA  128. CABDAB  129. CABDBA  130.  CADABB
131. CADBAB  132. CADBBA  133. CBAABD  134. CBAADB  135. CBABAD  136. CBABDA  137. CBADAB  138. CBADBA  139. CBBAAD  140.  CBBADA
141. CBBDAA  142. CBDAAB  143. CBDABA  144. CBDBAA  145. CDAABB  146. CDABAB  147. CDABBA  148. CDBAAB  149. CDBABA  150.  CDBBAA
151. DAABBC  152. DAABCB  153. DAACBB  154. DABABC  155. DABACB  156. DABBAC  157. DABBCA  158. DABCAB  159. DABCBA  160.  DACABB
161. DACBAB  162. DACBBA  163. DBAABC  164. DBAACB  165. DBABAC  166. DBABCA  167. DBACAB  168. DBACBA  169. DBBAAC  170.  DBBACA
171. DBBCAA  172. DBCAAB  173. DBCABA  174. DBCBAA  175. DCAABB  176. DCABAB  177. DCABBA  178. DCBAAB  179. DCBABA  180.  DCBBAA
 
Edwin
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