Question

The governor pf Punjab calls a meeting of 12 officers. In how many ways can they be seated at a round table?

Answer 1

@ganeshie8 @Michele_Laino

Answer 2

Find the number of ways in which 5 men and 5 women can be seated at a round table in such a way that no two persons of the same sex sit together.

Answer 3

please answer both of the questions.

Answer 4

how about YOU answer the questions?

for the first one:
there are 12 people - choose a seat - how many ways can that be filled ? ans = 12

now there are 11 people so the next seat - how many ways can THAT be filled?

so there are 12 * 11 ways the first 2 seats can be filled

Use your reasoning to work out how many way 12 seats can be filled....

Answer 5

please explain it wouldn't it be 11! ?

Answer 6

the first person to sit has 12 choices
the second has 11 choices (so there is 12 * 11 possible options for those 2)
the 3rd person has 10 choices (so there are 12* 11*10 ways that 3 can sit)

continue this logic for all 12 people.....

Answer 7

@MrNood you are wrong this is a circular permutation...can't you see its a round table?

Answer 8

@FlamePlaysMC

Answer 9

12 tables yes?

Answer 10

single round table

Answer 11

yeah how many chairs i meant

Answer 12

infinite isn't the issue here.

Answer 13

matters! what if there were less tables to seat on

Answer 14

there aren't brother its the governor!

Answer 15

hmm
12^12 is number of ways they can seat if we don't care about who seats where

Answer 16

nah...you are wrong on what base are you assuming that?

Answer 17

just my guts! but then i didn't include the governor himself

Answer 18

its 11! ways but need some confirmation and help....@xapproachesinfinity you are not good at permutation are you?

Answer 19

@ganeshie8 is good at this but he isn't online!

Answer 20

it is not 11!
i guarantee you that
say you have n people and we need k of them
but we don't care how they will seat
in how many way can they seat?

Answer 21

according to the wolf:

http://mathworld.wolfram.com/CircularPermutation.html

11! appears to be right if the governor is standing by himself....

Answer 22

I thought so but the answer provided at the end of my book contradict my theory!

Answer 23

@ganeshie8 !! need assistance asap!!

Answer 24

is it 12! then the governor is taking a seat too :)

Answer 25

no governor is a good guy he doesn't wants a seat he will just sit on the floor.

Answer 26

hahahaaa @Ehsan18 so wats the ans at ur book there?

Answer 27

19958400

Answer 28

ahhhh it is the clockwise vs counter-clockwise thing.....

11!/2 = 19958400

it is half because clockwise n counter-clockwise count as the same; even though it is not specified in ur prob there...

Answer 29

the wolf mentions that as "inequivalent when flipping the circle is allowed" n the eqn becomes

P'n = (n-1)!/2

Answer 30

may be but should just memorize it without concept?

Answer 31

the concept is fine but ur prob is not specific as to whether CW n CCW count as 1 or 2...it should have said something on that if its expecting u to give that ans

Answer 32

its probably because the governor is sitting on the floor so the table will be upside down and in upright positions both so there's how I will keep my concept steadfast!

Answer 33

@Ehsan18 i dont think dats wat ur teach has in mind when he wrote the prob! lol

but whatever works for u is good :) the prob is not very clearly defined.