Question

5 boys and 4 girls form a queue at the cinema. there are two brothers who want to stand together, the remaining 3 boys wish to stand together, and the 4 girls don't mind where they stand. In how many ways can the queue be formed?

Answer 1

if i'm not mistaken it should be 8P8 = 40320

Answer 2

incorrect

Answer 3

Is the answer 120?

Answer 4

the answer is 8640, but i have no idea how they got that!

Answer 5

not if the order amongst them can change

Answer 6

I think of it as 6 groups (4 girls, 2 brothers, 3 friends) for 6! orders
however, the 2 brothers can be in 2 different orders
3 guys in 3! ways
so 3! * 2 *6!

Answer 7

There are 2 (boy) groups and 4 individuals (girls), altogether 6 "units".
There are 6!=720 ways to arrange 6 units.
There are two ways to arrange the two brothers (AB or BA), and 3! ways for the three boys (3!)
Altogether there are therefore 720*2*6=8620 ways,by the multiplication rule.

Answer 8

@phi Sorry, it's 6 of course.

Answer 9

6P6 * 3! * 2!

Answer 10

typo!

Answer 11

6! * 3! * 2! is correct.

Answer 12

yes, 8640.

Answer 13

oh i seee thank you!

Answer 14

how come the girls don't count ie 4!

Answer 15

The girls count, but they're part of the 6!.

There's 6 different units of people 1 girl, 1 girl. 1 girl, 1 girl, 2 brothers, 3 friends.

Answer 16

oh i see