document.write( "Question 1173343: From the numbers 1,2,3,4,5,6,7,8, and 9, four different numbers are selected to form a four-digit number.
\n" ); document.write( "a.How much four-digit numbers can be formed?
\n" ); document.write( "b.How many four-digit less than 2,000 can be formed?
\n" ); document.write( "c.How many four-digit even numbers can be formed? \n" ); document.write( "
Algebra.Com's Answer #798560 by ikleyn(52781)\"\" \"About 
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document.write( "(a)  9 options for the most-left digit;\r\n" );
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document.write( "     8 remaining options for the next digit;\r\n" );
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document.write( "     7 remaining options for the next digit;\r\n" );
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document.write( "     6 options for the last digit.\r\n" );
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document.write( "     In all, there are  9*8*7*6 =  3024  such numbers.      ANSWER\r\n" );
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document.write( "(b)  \" Less than 2000 \"  means that the first digit is 1.\r\n" );
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document.write( "     Then there are 8 remaining options for the next digit;\r\n" );
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document.write( "                    7 remaining options for the next digit;\r\n" );
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document.write( "                    6 remaining options for the last digit.\r\n" );
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document.write( "     In all, there are  8*7*6 =  336  such numbers.       ANSWER\r\n" );
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document.write( "(c)  The last digit (\"ones\" digit) is any of four even digits 2, 4, 6 8, giving 4 options\r\n" );
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document.write( "     The \"tens\" digit is any of 8 remaining digits, giving 8 options;\r\n" );
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document.write( "     The \"hundreds\" digit is any of 7 remaining digits, giving 7 options;\r\n" );
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document.write( "     The \"thousands\" digit is any of 6 remaining digits, giving 6 options.\r\n" );
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document.write( "     In all, the number of options is  4*8*7*6 = 1344,  giving  1344 possible numbers.\r\n" );
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\n" ); document.write( "\n" ); document.write( "If you want to see many similar solved problems on PERMUTATIONS, see my lessons\r
\n" ); document.write( "\n" ); document.write( "    - Introduction to Permutations\r
\n" ); document.write( "\n" ); document.write( "    - PROOF of the formula on the number of Permutations\r
\n" ); document.write( "\n" ); document.write( "    - Simple and simplest problems on permutations\r
\n" ); document.write( "\n" ); document.write( "    - Special type permutations problems \r
\n" ); document.write( "\n" ); document.write( "    - Problems on Permutations with restrictions \r
\n" ); document.write( "\n" ); document.write( "    - OVERVIEW of lessons on Permutations and Combinations\r
\n" ); document.write( "\n" ); document.write( "in this site.\r
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\n" ); document.write( "\n" ); document.write( "Also,  you have this free of charge online textbook in ALGEBRA-II in this site\r
\n" ); document.write( "\n" ); document.write( "    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.\r
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\n" ); document.write( "\n" ); document.write( "The referred lessons are the part of this online textbook under the topic  \"Combinatorics: Combinations and permutations\". \r
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\n" ); document.write( "\n" ); document.write( "Save the link to this textbook together with its description\r
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\n" ); document.write( "\n" ); document.write( "Free of charge online textbook in ALGEBRA-II
\n" ); document.write( "https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson\r
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\n" ); document.write( "\n" ); document.write( "into your archive and use when it is needed.\r
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