SOLUTION: Hello, In class there are 8 boys and 10 girls. The teacher pairs the students randomly. What is the probability that 8 pairs are girl-boy pairs? How do I approach this? I

Algebra ->  Permutations -> SOLUTION: Hello, In class there are 8 boys and 10 girls. The teacher pairs the students randomly. What is the probability that 8 pairs are girl-boy pairs? How do I approach this? I       Log On


   

Question 1042925: Hello,
In class there are 8 boys and 10 girls. The teacher pairs the students randomly. What is the probability that 8 pairs are girl-boy pairs?
How do I approach this?
I was thinking maybe:
(8c1*10c1*7c1*9c1*...*2c2)/(18c2*16c2*...*2c2)
Thank you for your help and time.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
There are (8 C 1)*(10 C 1) = 8*10 = 80 ways to form a pairing of a boy and a girl.

This is out of 18 C 2 = 153 ways of picking 2 students.

The probability is therefore 80/153 = 0.52287581699347

Which is roughly 52.288%.
So about roughly half of the time, you expect a pair to consist of one boy and one girl.