indirect question

Question

I hope I got the terminology right, here is the case I want to ask about:

In an exercise, I have to find out what the protagonists say in which situation. The situation is described in a short sentence. Here is the sentence in question:

社員研修の制度が利用できないか聞くとき "When he asks if it wouldn't be possible to use the employee training program..."

What bothers me is the sole か. If I remember correctly, for indirect/embedded questions, か alone is used only if a question word is contained in the respective clause, like なん or どう. I can't see something like that being the case here, so I'd expect か どうか here. My textbook never taught me wether this "rule" gives you any leeway in omitting the どうか even though there's no such question word. Or maybe I misinterprete something here.

Answer 1

Are you sure there isn't either a と or an を missing after the か that is bothering you? That's the part that bothers me in your sentence.

But at any rate, the use of か by itself in cases like this is quite common, more so than かどうか which tends to be used in cases involving a binary "either ... or" choice, often to emphasize the fact that it's only one or the other. Your sentence would certainly work with かどうか in that respect, but I think that it would be overkill here given the broader context of the conversation that goes with this exercise, which you posted in a separate question. The focus isn't on whether the company training assistance programme can or cannot be used, but on the willingness of the speaker's boss to let him use that programme.

In more open-ended questions such as どれを選べばいいか迷ってる, or どこから始めたらいいかさっぱりわからない, for example, you couldn't use かどうか.