A soccer team has five girls and four boys. (All the team members are distinguishable.) How many ways can they stand in a row for a photograph, so that at least two of the girls are standing next to each other?

Guest Dec 19, 2019

#1**0 **

There are 8 ways to choose the two positions where the girls are standing, and C(5,2) ways to choose the two girls in those positions. There are then 7! ways to arrange all the other team members, so there are 8*C(5,2)*7! = 403,200 possible arrangements.

Guest Dec 19, 2019

#2**0 **

Hello! I'm just wondering, what does the "C" mean when you say C(5,2)? I know this but I forgot it already.

Guest Dec 19, 2019

#4**0 **

C(n,k) stands for the binomial coefficient: https://en.wikipedia.org/wiki/Binomial_coefficient

Actually, there are two ways to arrange the girls, so the number of arrangements is 2*403,200 = 806,400.

Guest Dec 19, 2019

#5**0 **

Ok, I see what it means and it's also incorrect, but I notice the problem asks for "at least" 2 girls next to each other, not JUST two girls.

Guest Dec 19, 2019

#6**0 **

**Please thank the answerer for their interest and never say that an answer is incorrect without giving a reason.**

The reason can be very simple. .... Like

My teacher says it is wrong,

or

The answer in the back of the book is such and such.

Always give the answerers as much knowledge about the question as what you have yourself.

Melody
Dec 22, 2019