Given that b<2k and g<2k, what is the probability that within the group of theatregoers there will be more girls than boys?
No Solution Yet  Submitted by Ady TZIDON 
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short amendment 

The constraint ( b<2k, g<2k) was unnecessary and stupid, introducing unnecessary noises.
The only valid restriction should be (b+g)<2k  i.e. not enough tickets to please all the students.
However, nothing prevented solving the sample (not restricted) by the simplest way:
P(gs get 5 tkts)=C(14,5)*C(6,3)/C(20,8)
P(gs get 6 tkts)=C(14,6)*C(6,2)/C(20,8)
P(gs get 7 tkts)=C(14,7)*C(6,1)/C(20,8)
P(gs get 8 tkts)=C(14,8)*C(6,0)/C(20,8)
P(gs get over 4 tkts)=sum of the results above=
I leave it to you to generalize for b, g, 2k; such that b+g<2k .
Rem: a consistent typo corrected following Charlie's remark.
Edited on October 14, 2014, 9:52 am
Posted by Ady TZIDON on 20141011 02:00:08 