Five people are to dine at a rectangular table but the host cannot decide on a seating arrangement in how many ways can the guests be seated?

1 Answer
Alan P.
Feb 14, 2016

#56xx5! =6720#

Explanation:

Arbitrarily calling one side of the table the "First Side" and labeling the others "Second", "Third" and "Fourth".

There is #1# arrangement that places #5# people on the "First Side"
and #3# arrangement that place #4# people on the "First Side"
and #6# arrangements that place #3# people on the "First Side"
and #10# arrangements that place #2# people on the "First Side"
and #15# arrangements that place #1# person on the "First Side"
and #21# arrangements that place #0# people on the "First Side"
for a total of
#color(white)("XXX")56 # seat arrangements

Arranging the 5 guests (starting by seating with the left-most seat on the "First Side") can be done in #5!# ways.

This gives #56xx5!# ways of seating the guests.

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