<PRE><B>Question 839205</B>
First, think about how many ways there
are for the 1 boy and the 1 girl to
sit together in the 8 seats
You can make 7 adjacent pairs out of
the 8 seats. That is the possible ways
they can sit together
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If you forget about these two, there are
{{{ 4 + 4 = 8 }}} ways to fill the 1st
seat, then there are {{{7}}} ways to fill the
2nd seat, {{{6}}} ways to fill the 3rd seat, etc
That is:
{{{ 8*7*6*5*4*3*2*1 = 40320 }}} ways to
seat the 4 boys and 4 girls in 8 seats
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Now subtract the 7 ways that the 1 boy and
1 girl can sit together
{{{ 40320 - 7 = 40313 }}}
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I think this is right- you might get a 2nd
opinion, though</PRE>