Question

In how many ways can 6 married couples sit in a row if no 2 women sit next to each other?

Answer 1

that means the possible order would be alternating right?

B G B....etc

or

G B G...etc

agree?

Answer 2

yes I believe so

Answer 3

then...it says 6 couples...so there are 3 men and 3 women.

the possible order for the 3 men would be 3!
and the possible order for the 3 women would be 3!

right?

Answer 4

no there are 6 men and 6 women & no 2 women can sit next to each other so what would you do for that? that's why i got stuck

Answer 5

you said 6 married couples....

Answer 6

oh wait yes. i stand corrected

Answer 7

so there are 6 men and 6 women

possible order for 6 men would be 6!
possible order for 6 women would be 6!

right?

Answer 8

yes. what do you do for the fact that no women can sit next to each other?

Answer 9

didn't i show you the illustration before? the order is

B G B G B G B G B G B G

and

G B G B G B G B G B G B

one order is 6!6! because there are 6! possible orders for the men and 6! possible orders for women. do you follow so far?

Answer 10

ya i have that already... but 2x6!x6! isn't correct

Answer 11

you sure?

Answer 12

yes

Answer 13

unless...there's another restriction....that the couples have to stay together....

Answer 14

otherwise the solution should be 2x 6!6!

Answer 15

they do have to stay together

Answer 16

then it really isn't 2(6!6!)

Answer 17

then what is it...?

Answer 18

nvm got it, thanks.