What is the criterion for distinguishing between subordinate matters and those intended for themselves in assisting with things, and is it permissible to wash a car that will be used for one permissible act and five forbidden acts, or ten permissible things and one forbidden one?

The difference between directly committing a sin and assisting in it is that the direct perpetrator is the one who commits the sin himself, while the assistant is the one who helps another person commit it. Assistance can be direct, such as someone serving alcohol or writing a usurious contract and witnessing it; these individuals incur sin. As for indirect assistance, it is like a receptionist at a usurious bank who is not directly involved in usurious transactions, but his work is not free from indirect assistance. However, washing a car for someone who will use it for an illicit purpose is permissible, unless it is known that his purpose for washing it is unlawful, such as to deceive with it; in that case, assistance is not permissible.