I know in the US at least it is not hard at all to find a family and even to select them. If they are in foster care they may bounce from home to home and never really be adopted (though I think babies have a better chance of being adopted from foster care). If you choose adoption (at least in the US) then all expenses are normally paid; with foster care they would not be. If you're sure you want to give the child up permanently, then adoption (possibly open if you want pictures/ updates) would probably be a better option.
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