ibento ni mousikomuno ga okureta noni, aki ga atte yokatta.

のに means “even though/ despite,” and it highlights a result that goes against expectation. It often carries a feeling of “surprisingly” or even “frustratingly,” depending on context.

• 遅れたのに、空きがあってよかった。 = “Even though I was late, I’m glad there was space.” (unexpectedly good outcome)
• けど is a milder “but/though” and doesn’t strongly imply surprise.
• が is a more formal or written-style “but,” often weaker than のに in expressing the “contrary to expectation” nuance.

You could say 遅れたけど here; it’s just less emphatic than のに. For very formal writing, にもかかわらず is another option.

No. They’re different:

• The first の (in 申し込むの) nominalizes the verb clause “apply” so it can function as a noun/subject.
• The second の is part of the conjunction のに (“even though”).

So the structure is: [イベントに申し込むの] が [遅れた] のに …

• 申し込むの: Verb nominalized with の. Very natural in speech for “the act of applying.”
• 申し込み: Noun “application.” Also natural: イベントへの申し込みが遅れた.
• 申し込むこと: More formal/abstract. In this specific “be late” pattern, こと sounds stiff or less idiomatic. Prefer 申し込むの or 申し込み.

All of these can work, but the most conversational here is the original with の.

No. You need a noun-like subject before が. Without の (or a noun like 申し込み), 申し込むが遅れた is ungrammatical. Correct options:

• 申し込むのが遅れた
• 申し込みが遅れた

空き (あき) is a noun meaning “vacancy/opening/availability.” Common patterns:

• 空きがある／ない = “there is/there isn’t an opening”
• 席が空いている = “a seat is free” (adjectival verb phrase) Use 空き when you talk about “openings” in the abstract; use 空いている to describe a specific thing as unoccupied (seat, room, time slot).

It’s the て-form of ある, linking the existence to the feeling:

• Pattern: [X があって] + よかった = “I’m glad there was X.” More generally: Vて + よかった expresses relief/satisfaction about a completed event.

Yes, but nuance changes:

• うれしい = “happy,” more about direct emotion.
• よかった = “I’m glad/relieved it turned out okay,” a bit more about the situation’s favorable outcome. Other near-synonyms: 空きがあって助かった (“that saved me”), 安心した (“I felt relieved”).

申し込む has two common patterns:

• Target/destination: Nに申し込む (イベントに、会社に、講座に)
• The thing you request/apply for: Nを申し込む (参加を、融資を、入会を) So:
• イベントに申し込む = apply to the event (target)
• イベントへの参加を申し込む = apply for participation (the action requested) Avoid イベントを申し込む, which is unnatural because the event itself is not the “requested action.”

Yes:

• 遅れたけど、空きがあってよかった。 (neutral “but”)
• 遅れたが、空きがあってよかった。 (more formal/written) They’re both fine but lack the stronger “despite (unexpectedly)” flavor of のに. For formal “despite,” use にもかかわらず.

The comma is just a natural pause; you can omit it in plain text. Clause order is typically:

• [Concessive clause]、Reversing it is possible but sounds awkward here; the concessive clause usually comes first.

Yes:

• イベントへの申し込みが遅れたのに、空きがあってよかった。 This shifts focus to “the application” as a thing, but the meaning and tone are the same.

Yes. The subject “I” is understood from context. If you need to be explicit, you can add 私は at the start, but it’s often unnecessary:

• 私はイベントに申し込むのが遅れたのに、空きがあってよかった。