5 persons are sitting in a round table in such way that tallest person is always
on the right side of shortest person,the no of such arrangements is
There are just 3! = 6 ways. In permutation word problems, when we
see the words "a round table", we are to consider that the round table
and chairs are placed on a large turntable such that rotating the
people, table, and chairs around does not change the seating arrangement.
If T is the tallest person, S is the shortest person, and A,B, and C
are the other 3 people, then here are all 6 of the ways.
T T T T T T
C S B S C S A S B S A S
B A C A A B C B A C B C
With a "round table", we can just consider that S and T
are always at the same fixed places so that T is to the
immediate right of S, and permute the other 3 around them.
That's why it's 3!.
["Round table" problems are not realistic because nobody
ever puts tables, chairs, and people on large turn-tables.
Nevertheless, that's the way to consider such problems.]
Edwin
