SOLUTION: 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?
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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? Answer by josmiceli(19441) (Show Source):
You can put this solution on YOUR website! 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) ways that 5 boys can sit this way
also ways the girls can sit
(2)
also ways for boys
and ways for girls
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In case (1), each of the ways the boys can sit
can be matched with ways the girls can sit
The same is true for case (2)
The total possible seating arrangements is:
