Surgeon's Question Thread

[Surgeon]

Having a mental blank here.. I just don't get this question.. Would appreciate someone pointing out my stupidity.

Question: Seven friends - 4 boys and 3 girls - sit in a single row on a park bench. If no boys sit next to one another, how many different seating arrangements exist for the 4 friends?

Here's what I thought.

Seating arrangement must be as follows: B G B G B G B

Shouldn't the options be (4!+3!+3!+2!+2!+1!+1!)?

The answer is 144, apparently :|

[b^3]

B G B G B G B
So for the first boy there is 4 choices, first girl there is 3 choices, now for the second boy there will be 4-1=3 choices e.t.c
So in terms of choices we have
|B| |G| |B| |G| |B| |G| |B|
|4| |3| |3|  |2| |2| |1| |1|
Arrangements = choices

[Shenz0r]

Sounds like one of those permutation questions from Methods.

[pi]

Sounds like one of those permutation questions from Methods.

Yep, yr11 Methods right there

+1, b^3

[Surgeon]

Ohhhh I was doing the factorial of each!

That explains it.

Can anyone please explain why doing the factorial of each doesn't work?

+1 b^3, thank you.