Answer to the Bedales lambs probability poser

OK, here it is: probability of 16 ewe lambs and 22 ram lambs from 19 ewes:
 
P(16/38) = 11,119,987,215/137,438,953,472
 
This comes out at approximately 0.08 or (if you will allow probability to be expressed as an approximate percentage, a double heresy as far as many mathematicians are concerned) 8%.
 
The winner of the approximate figure was Luke A. The winner of the exact figure was Michael Truss.
 
By Keith Budge, Headmaster, Bedales Schools

Bedales School is one of the UK’s top independent private co-education boarding schools. Bedales comprises three schools situated in Steep, near Petersfield, Hampshire: Dunannie (ages 3–8), Dunhurst (ages 8–13) and Bedales itself (ages 13–18). Established in 1893 Bedales School puts emphasis on the Arts, Sciences, voluntary service, pastoral care, and listening to students’ views. Bedales is acclaimed for its drama, theatre, art and music school. The Headmaster is Keith Budge.