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Using the letters  A and B, the following two-letter code words can be formed: AA, AB, BB, BA. Using the letters A, B, and C, how many different three-letter code words can be formed?

Sep 1, 2020

#1
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There are 18 three-letter words that can be formed.

Sep 1, 2020
#2
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No guest! That answer is not 18, and you know it could not possibly be such a large number!

Think of the word as three spaces:

______  _______ _______

Now, each value on top of the spaces is how many options we can choose from:

3             3              3

______  _______  _______

Now, multiply:

3 * 3 * 3

There! 27.

How could that possibly be 18? Last time I checked, 18 did not equal 27...

Still don't believe me? How many more can you find? Oh, so you found another one? Let me hear. ABCDEFGH? Lovely, maybe I forgot about that one....

:)

Sep 1, 2020
edited by ilorty  Sep 1, 2020
#3
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ilorty: Because you CAN repeat the letters, you have: 3^3 = 27 permutations.

AAA, AAB, AAC, ABA, ABB, ABC, ACA, ACB, ACC, BAA, BAB, BAC, BBA, BBB, BBC, BCA, BCB, BCC, CAA, CAB, CAC, CBA, CBB, CBC, CCA, CCB, CCC, Total No = 27 permutations

Sep 1, 2020
#4
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Oh dear, my teacher is going to hunt me down for such a mistake!

anyways, thanks for the reminder! I just edited my answer, happy?

ilorty  Sep 1, 2020