A dictionary of Confusable Phrases: More Than 10,000 Idioms and Collocations

open-armed • open-handed
open-armed —ready to receive people with enthusiasm:
There they are, all waiting open-armed for tourists to arrive.
When I traveled in April, the hotels were brim-full.
open-handed —treating people in a generous, liberal way:
Being an open-handed woman, Kathleen offered to read my
manuscript (which was still in the typewritten stage).
open house • open housing
open house —
1
. said of general hospitality and readiness to
welcome guests at any time: Their home was an open house
where the door was never locked and everyone was welcome.
2. a social event, such as a presentation, which everybody can
attend: The format of the meeting was an open house in which
the design concepts were presented for public review.
open housing —(U.S.) property that can be rented or bought
without restriction on racial or ethnic ground: The objection,
apart from prejudice, is usually economic because open hous-
ing may drive down values of real estate.
open question • open-end question
open question —an issue not yet finally decided that can still
be discussed: There was no clear resolution on this except to
note that this remains an open question.
Note: 
The expression is not equivalent in meaning to the phrase
open to question
— used of statements, assertions, etc. that are
doubtful and subject to challenge or disagreement: The govern-
ment have always known that the status of these islands is
open to question.
open-end question —(also: open-ended question) a question
so phrased as to encourage an expression of opinion (as dis-
tinguished from a simple negative or affirmative): The reading
test consists of open-end questions based on different texts of
various subjects and length.