How is the house mentioned in the question to be distributed among the ten children, and is it a right for all the children or only for the six children whose mother the sales contract was concluded for?

The entire inheritance goes to the sons by way of ta'sib (residuary inheritance) equally, and the brothers receive nothing because they do not inherit when a son is present, by consensus. Thus, the estate is divided into ten shares, with each son receiving one share.

As for the house, unless more details are provided about the nature of the contract, its date, the status of the disposer, and whether the wife took possession of the house before death, it is impossible to state anything definitively.