A couple with children of 3 boys and 5 girls decided to have s family
dinner in a reaturant. Two boys had s fight and resist of not sitting
togethre. They were sitting on a roung table and the couple would like
to sit beside each other.
a)how many possible ways that the two of the
brothers are not sitting together?
b)how many possible ways can you sit
the children or alternate seats?
1

a)how many possible ways that the two of the
brothers are not sitting together?
5 boys and 5 girls
(11­1)! 2! ­ 2!(10­1)! = 6 531 840
# of ways the
# of ways the
# of ways
# of ways
they can be 2 brothers
two brothers
the couple
seated in a can sit next to
can be
can be
round table each others.
rearranged rearranged
and the
couple
insist on
sitting
together.
2

b)how many possible ways can you sit
the children or alternate seats?
H W
B G 5!5!2! = 28 800
B
G # of ways the
# of ways the # of ways the
boys can be
girls can be
G couple can be
rearranged
rearranged
B rearranged
B
G G
B
3

4