Since some day is not an error (see below) , there is no actual error in the sentence
(1)[Most people] in the country (2)[would like] to own (3)[their house] (4)[some day].
When I first read the sentence, I thought the sentence would be much better with the adjective own before house in (3):
Most people in the country would like to own their own house some day
(as opposed to renting a house or just dreaming about owning a house). Note that user SevenSidedDie has aptly pointed out a reading that did not occur to me and which makes my objection largely based on a certain interpretation of the sentence. And this depends on how one uses or defines the verb own. In the USA, people are considered homeowners when they take out a loan on a house and repay the loan over a period of time, say 15 or 30 years. But there is a sense in which people do not really own their home until they have fully repaid the loan. Therefore my objection to (3) was based only on one reading of the sentence.
As to the idea that house
should be plural because we are talking about more than one house (that is, the 'most people' in this sentence do not live in a single house), this objection is answered by the fact that we can name an item in the singular even when we are talking about many of them. We can do this when we want to emphasize that everyone actually had one of the stated items, as in
Most students brought their lunch (not lunches) to school because they did not like the food in the school cafeteria.
Most people wash their car (not cars) when it is sunny outside.
You can use lunches and cars but you don't have to.
Most students brought their backpack (not backpacks) to school and set it down in front of them.
Note also that 'in the country' is ambiguous, and this can also affect one's interpretation of the sentence. Country
can mean both nation
. Without context, the sentence could be referring to 'most people in the nation' or 'most people in the countryside'.
As for the popular answer and much discussed issue regarding someday
versus some day
, when I read the sentence the first time, I did not notice any "error" regarding some day
. This is because there isn't one.
Some speakers and/or websites may wish to insist that one should use someday rather than some day when talking about "some unknown day in the future."
However, there is plenty of support for using some day with this meaning.
First and foremost is the Oxford English Dictionary (OED), which defines both one day and some day as
On an unspecified day in the future
and then gives example sentences from the past 500+ years. I will quote sentences from only the past 200 to 300 years.
Since it is important to realize that both one day and some day have the same meaning in this context, here are four sentences from the OED with one day:
1738 Swift Compl. Coll. Genteel Conversat. 57 I'll make you one Day sup Sorrow for this.
1872 J. Morley Voltaire i. 2 A gracious, benevolent, and all-powerful being, who would one day redress all wrongs and recompense all pain.
1945 T. Williams 27 Wagons Cotton 217 One day I will look in the mirror and I will see that my hair is beginning to turn grey.
2001 M. Ravenhill Mother Clap's Molly House ii. viii. 85, One day I'm just gonna up and go.
Here are four sentences from the OED with some day:
1796 F. Burney Camilla IV. vii. xiii. 196 There's no keeping him. I may be tempted else to knock his brains out some day.
1853 E. Bulwer-Lytton My Novel III. ix. xvii. 95, I hope to return some day what you then so generously pressed upon me.
1953 D. Whipple Someone at Distance xx. 176 ‘Some day’, she said to herself, ‘I shall be in a position where these little people will not dare to disrespect me.’
2002 Chicago Tribune 8 Apr. i. 2/5 He'll do just fine. The kid might even make federal judge some day.
Basically, one day and some day are interchangeable when they refer to an unknown future day. There is no valid rule based on actual usage that says one must use someday in this context. The Free Dictionary redirects a search for 'some day' to 'one day' but then says they are synonyms:
one day also some day
in the future I'd like to go to Mexico one day.
In addition, Collins dictionary online makes no distinction between 'some day' and 'someday' other than that there are two spellings:
some day or someday
at a date in the future that is unknown or that has not yet been decided
⇒ He said he wants to be a supervisor some day.
⇒ He took her left hand, hoping that it would someday bear a gold ring on the third finger.
⇒ I hope someday we'll have enough money to retire.
⇒ Some day I'll be a pilot.
There is no "governing board" of English. It is the speakers of English who determine usage and 'correct usage'. For 500 years or more, English speakers have been using both one day and some day to refer to some unknown day in the future. Folks who insist that it must be someday are making up a rule, or perhaps passing on an invalid rule that someone taught them.
Thus, there is no actual error in the original sentence, as you have given it, with no context and without our knowing what the textbook might be trying to demonstrate with the sentence.