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How many 3-letter words can we make from the letters A, B, C, and D, if we are allowed to repeat letters, and we must use the letter A at least once? (Here, a word is an arbitrary sequence of letters.)

 Apr 11, 2020
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In this case, it might be easier to count the number of total words and subtract the number of words that do not contain A.

 

There are 4*4*4=64 total words

There are 3 letters excluding A, so 3*3*3=27 words w/o A

64-27=37 possible words that contain A.

 Apr 11, 2020
edited by power27  Apr 11, 2020
edited by power27  Apr 11, 2020

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