document.write( "Question 1162135: Twelve presidents, 5 males and 7 females, attending a summit on climate decide to conclude the summit with a photo shoot. In how many ways different can they arrange themselves in a single row, if the males must be kept together?
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Algebra.Com's Answer #785852 by ikleyn(52906) $\"\"$ $\"About$

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document.write( "The answer is  8*5!*7! = 8*(5*4*3*2*1)*(7*6*5*4*3*2*1) = 4838400.\r\n" );
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document.write( "Explanation\r\n" );
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document.write( "We consider the group of 5 males as one object.\r\n" );
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document.write( "There are 8 possible positions/places for this group, considered as a single  object, in the row of 7 females.\r\n" );
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document.write( "    It gives the first factor of 8 in the formula.\r\n" );
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document.write( "Next, there are 5! ways to order 5 males inside their group.\r\n" );
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document.write( "    It gives the factor 5! in the formula.\r\n" );
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document.write( "Finally, there are 7! ways to order 7 females inside their group.\r\n" );
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document.write( "    It gives the factor 7! in the formula.\r\n" );
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document.write( "All these elementary arrangements are INDEPENDENT - - - so, we take the product of the factors to get the answer.\r\n" );
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\n" ); document.write( "\n" ); document.write( "See the 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
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\n" ); document.write( "\n" ); document.write( "    - Problems on Permutations with restrictions \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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