The Progressive-Japanese English Dictionary suggests 含める is the same as one meaning of 含む but it is not explained. Is this correct? I have two theories:
1. 含める= 含む when the latter means include/contain
This is based on the following examples
鉄分を含んだ水|water containing iron
その団体には女性2人が含まれている|The group includes two women.
And:
子供を含めて300人だ|There are 300 people, including the children.
郵送料を含めて5,000円だった|It cost 5,000 yen, postage included.
Which leads me to think:
水が鉄分を含む = 水が鉄分を含める (Water contains iron)
However we don't seem to find the following use: 鉄分を含める水
This leads me to (2):
2. 含める is used when the action of one party actively includes an object within in a group (which is grammatically an indirect object)
As in the following example:
彼らの名をリストに含めた|We included their names on the list.
Even in the following cases an indirect object seems to be implied
郵送料を含めて5,000円だった|It cost 5,000 yen, postage included.
私は税金を含めて月40万円の収入がある|I have an income of 400,000 yen a month before taxes.
Because they could easily be rewritten:
If I include postage, it cost 5000 yen.
If I include tax, my monthly income is 400,000 yen.
or,
Could we also write the following?:
郵送料を含んだ5,000円だった
私は税金を含んだ月40万円の収入がある
If so then these two verbs are interchangeable when the sense of include/contain is taken
Please let me know if my question is not clear.