Question 270349
There are only 2 ways if you don't care which girls and which boys
sit in which seats:
(1)
boys: seats 1,3,5,7,9
girls: seats 2,4,6,8,10
and
(2)
swap the boys and girls
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If you want all possible orders of boys and girls
(1)
{{{5*4*3*2*1 = 120}}} ways that 5 boys can sit this way
also {{{120}}} ways the girls can sit
(2)
also {{{120}}} ways for boys
and {{{120}}} ways for girls
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In case (1), each of the {{{120}}} ways the boys can sit
can be matched with {{{120}}} ways the girls can sit
{{{120*120 = 14400}}}
The same is true for case (2)
{{{120*120 = 14400}}}
The total possible seating arrangements is:
{{{14400 + 14400 = 28800}}}