document.write( "Question 156301: there are 4 men and 4 women to be seated in a row, and no 2 men or 2 women can sit next to each other. How many combinations of seating are there? \n" ); document.write( "

Algebra.Com's Answer #115234 by gonzo(654) $\"\"$ $\"About$

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not real sure but this is what i think.\r
\n" ); document.write( "\n" ); document.write( "no two men or two women can sit side by side so only can have\r
\n" ); document.write( "\n" ); document.write( "mwmwmwmw\r
\n" ); document.write( "\n" ); document.write( "or\r
\n" ); document.write( "\n" ); document.write( "wmwmwmwm\r
\n" ); document.write( "\n" ); document.write( "in the first set (mwmwmwmw) men can arrange themselves in 24 combinations and women can arrange themselves in 24 combinations so total combinations possible are 24 * 24 = 576.\r
\n" ); document.write( "\n" ); document.write( "in the second set (wmwmwmwm) same thing i.e. 24 * 24 = 576 possible combinations.\r
\n" ); document.write( "\n" ); document.write( "total number of combinations is sum of both sets = 1152.\r
\n" ); document.write( "\n" ); document.write( "worked this out with a smaller set (mwmw and mwmwmw) and it looks like it's correct.\r
\n" ); document.write( "\n" ); document.write( "combinations of men or women calculated as follows:\r
\n" ); document.write( "\n" ); document.write( "in the first woman position any of the 4 women can be in there.
\n" ); document.write( "in the second woman position any of the remaining 3 women can be in there.
\n" ); document.write( "in the 3d woman position any of the remaining 2 women can be in there.
\n" ); document.write( "in the 4th woman position the remaining 1 woman can be in there.
\n" ); document.write( "total possible combinations are then 4 * 3 * 2 * 1 = 24.\r
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