document.write( "Question 270349: In how many ways can a group of 5 boys and 5 girls be seated in a row of 10 seats if boys and girls must alternate in the row? \n" ); document.write( "

Algebra.Com's Answer #198088 by josmiceli(19441) $\"\"$ $\"About$

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There are only 2 ways if you don't care which girls and which boys
\n" ); document.write( "sit in which seats:
\n" ); document.write( "(1)
\n" ); document.write( "boys: seats 1,3,5,7,9
\n" ); document.write( "girls: seats 2,4,6,8,10
\n" ); document.write( "and
\n" ); document.write( "(2)
\n" ); document.write( "swap the boys and girls
\n" ); document.write( "-------------------------
\n" ); document.write( "If you want all possible orders of boys and girls
\n" ); document.write( "(1)
\n" ); document.write( " $\"5%2A4%2A3%2A2%2A1+=+120\"$ ways that 5 boys can sit this way
\n" ); document.write( "also $\"120\"$ ways the girls can sit
\n" ); document.write( "(2)
\n" ); document.write( "also $\"120\"$ ways for boys
\n" ); document.write( "and $\"120\"$ ways for girls
\n" ); document.write( "------------------------------
\n" ); document.write( "In case (1), each of the $\"120\"$ ways the boys can sit
\n" ); document.write( "can be matched with $\"120\"$ ways the girls can sit
\n" ); document.write( " $\"120%2A120+=+14400\"$
\n" ); document.write( "The same is true for case (2)
\n" ); document.write( " $\"120%2A120+=+14400\"$
\n" ); document.write( "The total possible seating arrangements is:
\n" ); document.write( " $\"14400+%2B+14400+=+28800\"$ \n" ); document.write( "

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