Not sure if Ninchux is correct....or if my answer is correct either...but here it is
10 players must each play 9 others = 90 games BUT two players are in each game 90 / 2 = 45 games total
5 players L must each play the other 5 players R = 25 games with L vs R
5 L must each play the other 4 lefties = 20 but two players in each game means 10 games with L vs L
Two right handed players would also be 10 games out of total 45 10/45 = 2/9
Anita must play 9 other players in the tournament 9 /45 = 1/5 of the games