document.write( "Question 832231: Find the number of words that can be made from the letters P,Q,R and S by using any number of letters without repeating any letter. \n" ); document.write( "
Algebra.Com's Answer #501925 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "We can pick the 1st letter any of 4 ways.\r\n" );
document.write( "For each of those ways to pick the 1st letter,\r\n" );
document.write( "there are 3 remaining letters we can pick for the 2nd letter.\r\n" );
document.write( "So that's 4×3 ways to pick the first two letters.\r\n" );
document.write( "For each of those 4×3 ways to pick the first 2 letter,\r\n" );
document.write( "there are 2 remaining letters we can pick for the 3rd letter.\r\n" );
document.write( "So that's 4×3×2 ways to pick the first three letters.\r\n" );
document.write( "Now there is only 1 letter remaining to pick for the 4th \r\n" );
document.write( "letter.\r\n" );
document.write( "So the answer is 4×3×2×1 which is called \"4 factorial\" and is written 4!\r\n" );
document.write( "and when we multiply it out we get 4×3×2×1 = 24.  So there are 24\r\n" );
document.write( "ways to arrange those four letters in different orders.\r\n" );
document.write( "Here's a check:\r\n" );
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document.write( "1. PQRS\r\n" );
document.write( "2. PQSR\r\n" );
document.write( "3. PRQS\r\n" );
document.write( "4. PRSQ\r\n" );
document.write( "5. PQRS\r\n" );
document.write( "6. PQSR\r\n" );
document.write( "7. QPRS\r\n" );
document.write( "8. QPSR\r\n" );
document.write( "9. QRPS\r\n" );
document.write( "10. QRSP\r\n" );
document.write( "11. QPRS\r\n" );
document.write( "12. QPSR\r\n" );
document.write( "13. RQPS\r\n" );
document.write( "14. RQSP\r\n" );
document.write( "15. RPQS\r\n" );
document.write( "16. RPSQ\r\n" );
document.write( "17. RQPS\r\n" );
document.write( "18. RQSP\r\n" );
document.write( "19. SQRP\r\n" );
document.write( "20. SQPR\r\n" );
document.write( "21. SRQP\r\n" );
document.write( "22. SRPQ\r\n" );
document.write( "23. SQRP\r\n" );
document.write( "24. SQPR\r\n" );
document.write( "  \r\n" );
document.write( "Yes there are 24.  But for many problems there are too many to check.\r\n" );
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document.write( "Edwin
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