in how many ways 9 people can be seated around a square table ,each side can accomodate a maximum of 4 dudes .

Question

the following question is with reference to the topic"permutations & combinations" from the subject -mathematics

Answer 1

There are more chairs (n=16) than people (k=9). From combination theory, the amount of different ways that chairs can be occupied is:
amount = (n over k) = n! / (k! * (n-k)!)) = 16*15*14*13*12*11*10*9*8 / (1*2*3*4....*9)
= 11'440.

When the chairs have been chosen, there are 9! permutations in the possible order the dudes can sit. 9!=1*2*3....*9=362880.

So the total amount of ways is:
11'440*362880=4'151'347'200

Luckily, when 9 people meet to be seated around a square table they do not discuss all possibilities before being seated! Usually, one chooses a seat (from the 16 available), then somebody who likes this person sits next to them (choosing one of the 15 remaining seats) and somebody else far away (14) etc...
Thus the result can also be computed by:
16 * 15 * 14 * ... * 8.= 4'151'347'200

Answer 2

Push the table to a corner and..........
Seat the 9 people, 3 on a side so that.... u need not worry about
all these permutation non-sense, ok???.....

Answer 3

16(ways where will the first person sit) * 15(ways where will the second person sit) * 14(ways where will the third person sit) .... *8((ways where will the last person sit)

= 16*15*14*13*12*11*10*9*8
= 4151347200

Answer 4

16 * 15 * .... 8 / 4 !

Answer 5

Its been too long since i studied PnC.
my ans is 3024 , 9 C 4
Anyway thanks for taking me back to my school days.