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?
I know that the answer is 27 from the answer sheet, but how? Can you please list the combinations? Thanks!
3*3*3
Yes, but can you list the combinations?
I'll get you started.
AAA
AAB
ABA
ABB
ABC
ACB
ACC
ACA
AAC
To determine how many different three-letter code words can be formed using the letters A, B, and C, we need to consider all possible combinations.
Since each letter can be placed in any of the three positions, we have three choices for the first letter, three choices for the second letter, and three choices for the third letter.
To find the total number of combinations, we multiply the number of choices at each position. So, 3 choices for the first position, multiplied by 3 choices for the second position, multiplied by 3 choices for the third position, gives us:
3 x 3 x 3 = 27
Therefore, we can form 27 different three-letter code words using the letters A, B, and C.
Here are all the possible combinations:
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
So, there are a total of 27 different three-letter code words that can be formed using the letters A, B, and C.