Question

In how many ways can 5 couples be seated in a row to take a photograph if:
(a) each woman and her husband must sit together?
my answer: 5!*2!=240
(b) No women sit on the end seats?
my answer: 5C2*8!*2=806400

are they correct?
@wio

Answer 1

For (a), you want to think about it as two tasks:
1) assign each couple a pair of seats.
2) count permutations for each couple.

Answer 2

I think you have (a) correct though.

Answer 3

For (b), does condition (a) still apply?

Answer 4

Yes, they're both correct

Answer 5

@wio no, part a and b are different

Answer 6

@sourwing really? but i don't know why part b is correct XD

Answer 7

(a) troubles me. Yes, 5! for assigning the seats to couples. Now let seat pair 1 be MF or FM. Similarly, seat pair 2 can be MF or FM...giving 2^5 possibilities even after the permutations are counted.
a total of n! 2^5 .

Answer 8

For part (b) you should
1) chose women to be on the end
2) count permutations for women on the ends
3) count permutations for remaining people in remaining seats

Answer 9

So, only men can seat at the end seat.
5 ways for the first seat, and 4 ways for the last seat. You have 8 people left of permute. so 5 * 8! * 4 = 806,400

Answer 10

Replace women with men in what I said before.

Answer 11

@douglaswinslowcooper i don't understand 2^5...
@wio permutation?!
@sourwing got it

Answer 12

permutations... number of ways to shuffle them around.

Answer 13

when you permute a whole group, it collapses into a factorial.

Answer 14

a permutation of n objects is an arrangement of the objects in a definite order............
but this question is arrangement?

Answer 15

wow many people in this post...

Answer 16

The coupoes are permuted, giving N! = 5!,
but within each pair seated they could be MF or FM, two possible orderings and there are five places with 2 orderings, giving a multiple of 2^5 more distinguishable combinations.

Answer 17

The seats are distinct.

Answer 18

So Sam, Jon, Joe is distinct from Jon, Sam, Joe

Answer 19

@wio yes
@douglaswinslowcooper i also do in this way..

Answer 20

Because husband and wife must sit together, we have effectively only five "seats," with two configurations per seat MF or FM.

Answer 21

This question can be summed up as \(5P2 \times 8P8\)

Answer 22

@wio the answers are still the same -.-
different method? or permutation must be used in this question?

Answer 23

It is the same solution, it is just a very concise method.

Answer 24

oh i see

Answer 25

(a) each woman and her husband must sit together?
my answer: 5!*2!=240

this is incorrect

Answer 26

@janaki.t23 why?

Answer 27

correct answer :-
5!(2!*2!*2!*2!*2!)

each 2! represents permutation for each couple

Answer 28

5! * 2^5 ?
ohh...it seems make sense...

Answer 29

@janaki123 Thank you.