[NotJustAnotherPrettyFace]

Are the women assigned to these various houses or do they choose?

[NYC GOP Chick]

Sort of a combination of both. Before starting first year, if you know in advance in which house or on which part of campus you want to live, you can usually request it on the housing form. And, if necessary, you can move during the year. After the first year, you pretty much have free choice in where you want to live, although if too many people want the same house, you might get your second or third choice.