What percent gets rejected by all?

There’s an unknown percentage of applicants who only apply to one or a few BS on purpose because they have great local options and opt not to go to BS if they can’t get in one of the selected few. And there are the ones who “desperately” want to attend a BS but don’t cast a net wide enough to land an offer on M10. I would guess the percentage you are looking for would be greater than its counterpart in college admission because everyone who applies to college arguably needs to go to a college while not everyone who applies to BS necessarily needs to go to a BS.