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?
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.
Hello! I'm just wondering, what does the "C" mean when you say C(5,2)? I know this but I forgot it already.
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.
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.
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My teacher says it is wrong,
The answer in the back of the book is such and such.
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