Since all of the "number of things" words all follow the same pattern (number plus つ), you really just have to remember the part before the つ (and then remember that the つ is in all of these). All of the readings are the kun'yomi reading, which means we'll have to use a mnemonic to remember them (you know the on'yomi reading of the kanji portion).
What thing do you have three of? The three things that you have are actually three versions of yourself. "Who is the real one?" you ask yourself. "It's me!" "Wait, no, it's me!" Just remember that there are three of you, and they're all saying "me me me me me" to try and prove that they're the real you.
You will hear three choices.
Please put three balls in here.
I got three mosquito bites.