We calculate the numerator of the probability, which is the number of
successful possibilities, of 3 girls and 1 boy.

The number of choices of 3 girls out of 14 girls, (14 choose 3), is C(14,3)

For every choice of 3 girls,

The number of choices of 1 boy out of 10 boys is (10 choose 1) or C(10,1)

So there are c(14,3)·C(10,1) choices of 3 girls and 1 boy.
---------
We calculate the denominator of the probability, which is the number of
all possibilites, successful or not, of any 4 people from the 14+10 or 24
people.

That's the number of choices of 4 people out of 24 people, (24 choose 4), 
or C(14,3)

The desired probability is therefore

       C(14,3)C(10,1)     364·10     3640      260
       —————————————— =  ———————— = ——————— = ————— ≈ 0.3425559947  
           C(24,4)        10626      10626     759

Edwin