【drop out】 —

1. leave a school, etc. before the end of the course:

• He has dropped out, and won’t attend college any more.

2. (coll.) withdraw (from an undertaking):

• You can 【drop out】 from the rat race, hoping that you can make it on your own.

3. come out:

• As she picked up the envelope, a key dropped out.

【fall out】 —

1. (Military) leave the ranks:

• At the end of the parade, the battalion fell out.

2. quarrel:

• We’re not going to 【fall out】 over this, are we?

3. come to pass; happen:

• It fell out that the men were not needed.

4. = 【drop out】 3:

• A little roll of dollar-notes fell out upon the ground.