Question Permutation and Combination (S1)

[zwitterion7]

Can some one please solve this question.

In how many ways can a committe of four men and four women be seated in a row if
no one is seated next to a person of the same gender?

 

[zwitterion7]

okay i found the answer. (4!4!2!) =)

 

[zwitterion7]

But can someone please explain this to me, i dont get how we reach the answer.

 

[ahmed t]

well u can have
MFMFMFMF
so the F can be arranged in 4!
and the M can be arranged in 4!
and remember we can have
FMFMFMFM
so we times by two since the M's and the F's can be interchanged

 

[ahmed t]

oh by the way F is female and M is male

 

[zwitterion7]

Thankyou.
But if they are arranged in 2! ways wont two men or women come together, like, FMMF... or something like that?

 

[ahmed t]

no,
u are simply changing the positions of all males with a female
so there will be nothing of that sort

 

[ahmed t]

anything else??

 

[hallaballa]

taking the males first
M M M M
they can be seated in any way
i.e 4!
now we have to position the womwn so no gernder would be next to eachother
It could be either FMFMFM or MFMFMF
so for females it''s 4!+4! ( you got to notice that all females can be seated on either side of every man bot only four men and four woman)
so here goes the answer
4!x(4!+4!)=4!x4!x2