SOLUTION: In how many ways can the letters of the word CAT be arranged to form three-letter words, if you are permitted to repeat a letter any number of times?

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Question 946333: In how many ways can the letters of the word CAT be arranged to form three-letter words, if you are permitted to repeat a letter any number of times?
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
We can choose the first letter 3 ways.

For each of those 3 ways to choose the first letter,
we can choose the 2nd letter also 3 ways.
That's 3x3 or 9 ways to choose the first 2 letters.

For each of those 9 ways to choose the first 2 letters,
we can choose the 3rd letter also 3 ways.
That's 3x3x3 or 9x3 or 27 ways to choose the 3 letters.

Answer: 27

Here are all 27 arrangements:

 1. CCC
 2. CCA
 3. CCT
 4. CAC
 5. CAA
 6. CAT
 7. CTC
 8. CTA
 9. CTT
10. ACC
11. ACA
12. ACT
13. AAC
14. AAA
15. AAT
16. ATC
17. ATA
18. ATT
19. TCC
20. TCA
21. TCT
22. TAC
23. TAA
24. TAT
25. TTC
26. TTA
27. TTT

Edwin