1. ## lost

how many ways can we arrange a row of four girls followed by four boys if girls must sit togther and boys must sit together?

i know stuiped question i just cant figure it out lol

2. Hello, scrappy!

How many ways can we arrange a row of four girls followed by four boys
if girls must sit togther and boys must sit together?

. . $\displaystyle \underbrace{G\:G\:G\:G}_{\text{4! ways}}\,\underbrace{B\:B\:B\:B}_{\text{4! ways}}$

Answer: .$\displaystyle 4! \times 4! \:=\:24 \times 24 \:= \:576$ ways

3. Originally Posted by Soroban
Hello, scrappy!

. . $\displaystyle \underbrace{G\:G\:G\:G}_{\text{4! ways}}\,\underbrace{B\:B\:B\:B}_{\text{4! ways}}$

Answer: .$\displaystyle 4! \times 4! \:=\:24 \times 24 \:= \:576$ ways
What happened to $\displaystyle BBBBGGGG$?

which doubles the number of ways.

RonL

4. Originally Posted by CaptainBlack
What happened to $\displaystyle BBBBGGGG$?

It's a matter of interpretation, I guess, but I did give it some thought.

"How many ways can we arrange a row of four girls followed by four boys . . . "
. . I read that to mean in that order.

If they meant $\displaystyle GGGGBBBB$ or $\displaystyle BBBBGGGG$, why use the phrase "followed by"?

Wouldn't it have said, "In how many ways can we arrange a row of four girls and four boys
. . if girls must sit togther and boys must sit together?"

5. Originally Posted by Soroban
It's a matter of interpretation, I guess, but I did give it some thought.

"How many ways can we arrange a row of four girls followed by four boys . . . "
. . I read that to mean in that order.

If they meant $\displaystyle GGGGBBBB$ or $\displaystyle BBBBGGGG$, why use the phrase "followed by"?

Wouldn't it have said, "In how many ways can we arrange a row of four girls and four boys
. . if girls must sit togther and boys must sit together?"
Yes, I guess that your interpretation fits the question better than mine,
must resolve to read the questions more carefully for the rest of the day

RonL