Arrangement in a circle (1 Viewer)

[cutemouse]

Three men and three women are to be seated at a round table.
How many seating arrangements are possible if each of the men is to have a woman seated either side of them?

An explanation would also be great.

Thanks

 

[x3.eddayyeeee]

is the answer 36?

 

[shady145]

so they are sat goin male, female, male, female...
so i positioned a man.
number of different ways they women can then sit them selves amongst the men = 3! ways
number of ways for remaining men to sit = 2!
number of spots for positioned guy to be positioned = 5 other ways
3!x2!x5
however i hate this topic XD and may be wrong

 

[scardizzle]

Consider a straight line of men alternating with women

MFMFMF

if this were made into a circle it would the perscribed arrangement so men can be arranged 3! ways and women can be arranged 3! since it is a circle we do not need

therefore total arrangement is = to 3! x 3! = 36

not sure if this is right someone please correct me if i'm wrong

EDIT: hmm but its a circle so rotating eliminates certain permutation...

giving this another go consider making a man the starting point number of permutations is 3!x2! and that's it?

 

[x3.eddayyeeee]

so they are sat goin male, female, male, female...
so i positioned a man.
number of different ways they women can then sit them selves amongst the men = 3! ways
number of ways for remaining men to sit = 2!
number of spots for positioned guy to be positioned = 5 other ways
3!x2!x5
however i hate this topic XD and may be wrong

i think this is more right.
but do we need to multiply by 5?
although the first male is in a different spot, some will become the same arrangement only rotated.

 

[Timothy.Siu]

Three men and three women are to be seated at a round table.
How many seating arrangements are possible if each of the men is to have a woman seated either side of them?

An explanation would also be great.

Thanks

arrange the men around the table. 3!/3
slot the women between them, 3!

so, its 3!/3 x 3!

 

[cutemouse]

Answer is 12... =\

 

[cutemouse]

arrange the men around the table. 3!/3

Thanks, but why do you divide by 3 there?

 

[Timothy.Siu]

because its a round table, i.e. circle.

 

[scardizzle]

because its a round table, i.e. circle.

this means 3 out of the 3! permutations are the same since you can rotate the circle

 

[cutemouse]

because its a round table, i.e. circle.

Ahh yes, thank you