document.write( "Question 930337: Consider a list of randomly generated 4-letter \"words\" printed on a paper. The letters cannot be repeated. \r
\n" ); document.write( "\n" ); document.write( "(a) At least how many of these \"words\" should be printed to be sure of having at least 7 identical \"words\" on the list? \r
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Algebra.Com's Answer #564898 by Edwin McCravy(20060) $\"\"$ $\"About$

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(a) At least how many of these \"words\" should be printed to be sure of having at
\n" ); document.write( "least 7 identical \"words\" on the list?
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document.write( "There are 26 ways to choose the first letter, 25 to choose the 2nd letter, 24\r\n" );
document.write( "ways for the 3rd and 23 for the 4th, so there are 26*25*24*23 = P(26,4)= 358800\r\n" );
document.write( "possible \"words\".\r\n" );
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document.write( "If there were 6*358800 or 2152800 words on the list, there would be a very\r\n" );
document.write( "slight chance that there were exactly 6 duplicates of each word.  However to\r\n" );
document.write( "eliminate that rare case, if there were 1 more word, or 2152801, on the list,\r\n" );
document.write( "there would necessarily be 7 duplicates of some word.\r\n" );
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document.write( "Answer: 2152801.\r\n" );
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\n" ); document.write( "(b) At least how many identical \"words\" are printed if there are 2870401 \"words\"
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document.write( "We divide 2870401 by 358800 \r\n" );
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document.write( "             8\r\n" );
document.write( "358800)2870401\r\n" );
document.write( "       2870400\r\n" );
document.write( "             1\r\n" );
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document.write( "We get 8 with 1 remainder.\r\n" );
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document.write( "So there is a slight chance that the 2870401 consists of exactly 8 duplicates of\r\n" );
document.write( "each of the 358800 words, plus 1 more word.  So there are at least 9 duplicates\r\n" );
document.write( "of some word on the list.\r\n" );
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document.write( "Edwin

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