SOLUTION: 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 w

Question 1024774: 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?
Answer by ikleyn(52781) (Show Source): You can put this solution on YOUR website!
.
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?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~

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.

RELATED QUESTIONS
seven guests are invited to dinner. How many ways can they be seated at a dinner table if (answered by jim_thompson5910)

There are four visitors in a party. There are two tables with two seats each. In how many (answered by Edwin McCravy,ikleyn)

Dinner guests are to be seated at 10 round tables labeled from A to J. Table A has 21... (answered by akumpo)

This might be in the wrong section but here it is: At a party, 2/3 of the guests drank (answered by josgarithmetic)

How many ways can 25 people be seated in a round table of there are 15 chairs? (answered by ewatrrr)

1. From a class of 40 students 8 students will be chosen to join the science field trip.... (answered by ikleyn)

The seats at a round table are numbered from 1 to 7. Find the number of ways in which a... (answered by rothauserc)

The same number of guests are seated at each of 11 large tables. There are 4 guests... (answered by Edwin McCravy)

In how many ways can an event organizer seat nine guests around a... (answered by MathLover1)