document.write( "Question 205863: How many three digit numbers can be constructed using the digits 1,2,3,4 and 4 if the same digit cannot appear twice in a row in any of the numbers?\r
\n" ); document.write( "\n" ); document.write( "(A)60 (B)65 (C)80 (D)120 (E)None of these \n" ); document.write( "

Algebra.Com's Answer #155508 by Edwin McCravy(20060) $\"\"$ $\"About$

You can put this solution on YOUR website!
How many three digit numbers can be constructed using the digits 1,2,3,4 and 4 if the same digit cannot appear twice in a row in any of the numbers?
\n" ); document.write( "

\r\n" );
document.write( "Only the digit 4 can appear twice, but not twice in\r\n" );
document.write( "a row, so the only ones with two 4's are these 3:\r\n" );
document.write( "\r\n" );
document.write( "414, 424, and 434 \r\n" );
document.write( "\r\n" );
document.write( "The rest have 3 different digits:\r\n" );
document.write( "\r\n" );
document.write( "There are 4 ways to select the first digit.\r\n" );
document.write( "For each of those, there are 3 remaining digits\r\n" );
document.write( "to place for the second digit,\r\n" );
document.write( "Foe each of the ways to place the first 2 digits, \r\n" );
document.write( "there are 2 ways to place the last digit.\r\n" );
document.write( "\r\n" );
document.write( "So that's 4*3*2 or 24 ways.\r\n" );
document.write( "\r\n" );
document.write( "So that's a total of 3 + 24 or 27 ways.\r\n" );
document.write( "\r\n" );
document.write( "Checking:\r\n" );
document.write( "\r\n" );
document.write( " 1. 123\r\n" );
document.write( " 2. 124\r\n" );
document.write( " 3. 132\r\n" );
document.write( " 4. 134\r\n" );
document.write( " 5. 142\r\n" );
document.write( " 6. 143\r\n" );
document.write( " 7. 213\r\n" );
document.write( " 8. 214\r\n" );
document.write( " 9. 231\r\n" );
document.write( "10. 234\r\n" );
document.write( "11. 241\r\n" );
document.write( "12. 243\r\n" );
document.write( "13. 312\r\n" );
document.write( "14. 314\r\n" );
document.write( "15. 321\r\n" );
document.write( "16. 324\r\n" );
document.write( "17. 341\r\n" );
document.write( "18. 342\r\n" );
document.write( "19. 412\r\n" );
document.write( "20. 413\r\n" );
document.write( "21. 414\r\n" );
document.write( "22. 421\r\n" );
document.write( "23. 423\r\n" );
document.write( "24. 424\r\n" );
document.write( "25. 431\r\n" );
document.write( "26. 432\r\n" );
document.write( "27. 434\r\n" );
document.write( "\r\n" );
document.write( "Edwin

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

\n" );