Otoko Hime to Mahou no Lamp

[From ShoujoMagic]:

This one volume work is a collection of selected stories from Kayono's "Arabian Nights" series.

1) Princess Man & the Magic Lamp -
Princess Sonia has been kidnapped and is being forced into a political marriage. "By no means will I lead such a life!" she proclaims, and then escapes from the castle and has a fateful encounter with Sinbad! At first she thinks she's jumped out of the frying pan and into the fire, because Sinbad seems like the worst man alive, but then they embark on a journey to seek out the "magic lamp"!?

2) Tearful Madonna.
Mink is a beautiful professional killer whose mission is to sneak into the castle of the Vampire Noa Tribe to assassinate their leader Orion.

3) The Beautiful Face Tribe.
Rin pretends to be a rich girl in order to marry a wealthy man and save her father from a 100,000,000 yen debt. However, she must first choose from one of the three brothers... The oldest is a singer for a rock band, the second son is a fantastic chief, and the third is a high-schooler too shy to speak yet wishes to become an actor. All have a tender heart; so, which will she choose... or will she sacrifice her father and her future by telling this family the truth about her intentions.