The correct answer is: in.
The preposition “in” is used to indicate a location or position inside something. In this case, the children are being placed in foster care, which is a type of temporary living arrangement for children who cannot live with their biological parents.
The other options are incorrect because they do not make sense in the context of the sentence. The preposition “to” is used to indicate a destination or goal. The preposition “of” is used to indicate possession or ownership. The preposition “by” is used to indicate a means or method. The preposition “for” is used to indicate a purpose or reason.
Here are some examples of how the other prepositions could be used in a sentence:
- The children are going to foster care.
- The children are the of foster care.
- The children are being cared for by foster parents.
- The children are in foster care because their parents cannot take care of them.