+0  
 
+3
131
4
avatar+44 

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
avatar
0

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

 Sep 1, 2020
 #2
avatar+1039 
+1

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
avatar
0

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
avatar+1039 
0

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

14 Online Users

avatar
avatar