Question

Six friends, four boys, and two girls went to a movie theater. They wanted to sit in a way so no girl sits on either first or last chair. How many such arrangements are possible?

Answer 1

Answer: 5 valid arrangements

Step-by-step explanation:

This depends on whether the boys or girls swapping places are considered unique solutions.  I'm going to assume that is no, because there would be an unrealistic amount of solutions if it is true.

Assuming G = girl and B = boy, these are the possible arrangements.

(I will bold the valid solutions).

GGBBBB

GBGBBB

GBBGBB

GBBBGB

GBBBBG

BGGBBB

BGBGBB

BGBBGB

BGBBBG

BBGGBB

BBGBBG

BBBGGB

BBBBGG

Thus, there are 5 valid arrangements.

Hope it helps <3

Answer 2

Answer:

12 different arrangements because the roles of the girls could be switched around.

Step-by-step explanation:

b = boys

g= girls

1:

bggbbb

2:

bbggbb

3:

bbbggb

4:

bgbbgb

5:

bgbgbb

6:

bbgbgb

Hope this helped! Brainliest would be appreciated :)