Problem Solving

5 boys and 4 girls have to stand in a line such that no two girls are next to each other. how many possible ways ?

could you please post choices

let us consider the 2 girls are together then

GG BGBGBBB
GG GBGBBBB

which gives 2*8*5!*2!=3840.

now the 5 boys and 4 girls can be arranged in

BGBGBGBGB
GBGBGBGBB

2*5!*4!=5760

there fore no two girls sit together is 5760-3840=1920 ways

1440 x 6 = 8640 ways

sibbineni wrote: =1920 ways

Incorrect.

cris wrote: 1440 x 6 = 8640 ways

Incorrect.

true. 17,280?

Where is this question from?

Also, would you please post the actual question (the one you posted is too ambiguous, we need the original language to solve) and the answer choices?

Based on what you posted, there's no way that this would be an actual GMAT question - there are too many ways in which it can be interpreted.

cris wrote:true. 17,280?

Incorrect

Keep trying !

Stuart Kovinsky wrote:Where is this question from?

Also, would you please post the actual question (the one you posted is too ambiguous, we need the original language to solve) and the answer choices?

Based on what you posted, there's no way that this would be an actual GMAT question - there are too many ways in which it can be interpreted.

5 boys and 4 girls have to stand in a line so that no two girls are next to each other. How many distinct arrangements are possible. ?

Lets give each boy and girl a name just to make it more clear

B1 B2 B3 B4 B5 - boys
G1 G2 G3 G4 - girls

I don't have the 5 answer choices. If you don't want to solve the question without the answer choices that is ok !

Answer is 7680...

mmm I still think it has to be 17,280. I dont think that there is another way in which they can be seated with out being 2 girls together...

BGBGBGBGB
BBGBGBGBG
GBGBGBGBB
GBBGBGBGB
GBGBBGBGB
GBGBGBBGB

Update
---------------------------------------
I found 3 oher ways:

BGBBGBGBG
BGBGBBGBG
BGBGBGBBG

25,920 :D

Well, not entirely sure but how about 6c4*5!*4!= 43,200 .. If it is right I will give my explanation for it.

Regards

cris wrote:mmm I still think it has to be 17,280. I dont think that there is another way in which they can be seated with out being 2 girls together...

BGBGBGBGB
BBGBGBGBG
GBGBGBGBB
GBBGBGBGB
GBGBBGBGB
GBGBGBBGB

You are missing out on many more possibilities like BGBGBBGBG or BGBGBGBBG or GBBGBGBBG or GBGBBGBBG .. there is a specific way to solve such questions, will write down those steps once my answer is confirmed.

Regards

Yep, Gabriel you are right, I have several more ways missing.

There has to be an easiest way than figuring out all the ways...this will def. take me more than 2 minutes...

I am sure you got the correct answer gabriel, you master these combination and permutations questions :)

Hi , I feel the answer should be 43200 distinct ways!. if my answer is correct I will explain you the procedure ! This is just one of the normal question in Perm and Combi.


Thanks
Senthil L