In Japanese, I have encountered 3 words for selecting or making a choice (so far).
彼はよい奥さんを選んだ。
He chose a good wife.
それでも、早期の退職を選択する人は多い。
Nevertheless, many are choosing early retirement.
例文の選定がまずかったです。
The choice of example sentence wasn't wise.
(Sample sentences are from JDIC:ED)
Are there any differences between the three? Or are they generally interchangeable?
Your first example is 選{えら}んだ, which is from the verb 選ぶ. It's the Japanese-origin word for "choose" and differs mostly by its formality compared to Chinese-origin words.
選択 is a simple choice. Pick a card, pick your classes, choose an answer on a test, or, as in your example, choose early retirement.
選定 is a choice with purpose. You choose something to match a set of criteria. You look at the choices, judge them each, and make the decision with regard to what you feel is the most appropriate one. For example, 議員を選定する. An example here is "購入機種の選定会議." It has more of an "official" flavor and is quite formal. It might be helpful to think of it as something that goes through a selection process. On the site I mentioned previously, a key distinction in the descriptions is in the choice of words for the actual verb: with 選択 it uses 選び出す, but with 選定, it uses 決める. This reinforces the idea of one being a mere choice while one is more elective. I'm sorry if this explanation is hard to follow but I'm straining to explain what is essentially in English the difference between choose and choose.
You asked separately why you would not use 選定 for an answer on a test. Think of it this way. When you're choosing answers on a test, you may be weighing each choice against certain conditions, but ultimately you're not really "deciding" which one is best. You're deliberating which one seems like the right answer. But your choice could be wrong. Because of the correct/incorrect nature you're choosing an answer in the lightest sense of the word, no matter how hard you think about it. With 選定 it's more about choosing one of several valid options and making a decision about which is most appropriate. For example, if you were to use 選定 on a test question, it would sound to me like you were choosing a test question or answer to be used as a representative or some kind in some compendium of example test questions and answers, trying to decide which ones to include in the collection.
It should be clear, then, that 選択 and 選定 are not interchangeable. 選ぶ on its own is not formal at all and can be kind of excluded on that basis, though you can probably use it (with the right level of formality) to mean the same thing as the other two. 選択 is for things where the judgment and criteria aren't as important as the act of choosing in itself, while 選定 emphasizes the meaning and purpose behind a choice.
