document.write( "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? \n" ); document.write( "

Algebra.Com's Answer #577321 by Edwin McCravy(20055) $\"\"$ $\"About$

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We can choose the first letter 3 ways.\r\n" );
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document.write( "For each of those 3 ways to choose the first letter,\r\n" );
document.write( "we can choose the 2nd letter also 3 ways.\r\n" );
document.write( "That's 3x3 or 9 ways to choose the first 2 letters.\r\n" );
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document.write( "For each of those 9 ways to choose the first 2 letters,\r\n" );
document.write( "we can choose the 3rd letter also 3 ways.\r\n" );
document.write( "That's 3x3x3 or 9x3 or 27 ways to choose the 3 letters.\r\n" );
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document.write( "Answer: 27\r\n" );
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document.write( "Here are all 27 arrangements:\r\n" );
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document.write( " 1. CCC\r\n" );
document.write( " 2. CCA\r\n" );
document.write( " 3. CCT\r\n" );
document.write( " 4. CAC\r\n" );
document.write( " 5. CAA\r\n" );
document.write( " 6. CAT\r\n" );
document.write( " 7. CTC\r\n" );
document.write( " 8. CTA\r\n" );
document.write( " 9. CTT\r\n" );
document.write( "10. ACC\r\n" );
document.write( "11. ACA\r\n" );
document.write( "12. ACT\r\n" );
document.write( "13. AAC\r\n" );
document.write( "14. AAA\r\n" );
document.write( "15. AAT\r\n" );
document.write( "16. ATC\r\n" );
document.write( "17. ATA\r\n" );
document.write( "18. ATT\r\n" );
document.write( "19. TCC\r\n" );
document.write( "20. TCA\r\n" );
document.write( "21. TCT\r\n" );
document.write( "22. TAC\r\n" );
document.write( "23. TAA\r\n" );
document.write( "24. TAT\r\n" );
document.write( "25. TTC\r\n" );
document.write( "26. TTA\r\n" );
document.write( "27. TTT\r\n" );
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document.write( "Edwin

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