.
There are 11 guests in a party
1)In how many ways can the guests be seated at a round table with 15 numbered seats?
2)In how many ways can the guests be seated at a round table with 15 identical seats?
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1. The first guest can choose any of 15 seats.
The second guest can choose any of 14 remaining seats.
. . . .
The 11-th guest can choose any of (15-10) = 5 seats.
In all, there are 15*14*13* . . . *5 =
ways/options.
2. If the seats are non-numbered (i.e. identical), we can not and do not make distinguish
between configurations that differ by the turning / circular translation of all seats around the table
in 1, 2, 3, . . . , 15 positions. So, we need to divide
by 15.
Thus the answer is
.
= 14*13*12* . . . *5.