There are 3 bags and 5 different marbles. In how many ways can the marbles be put into the bags?
(disclosure - the question is one of many in a teacher prep study guide. I am taking the qualification exam for teaching middle school math next month.)
The answer and explanation for the above was given as 3^5 = 243.
Earlier on, the book offered the distinction between say "3 kids of a group of ten are being chosen to play...." and the more specific "3 kids of 10 are being chosen for pitcher/catcher/first base" - the former being a lower number since it's not for specific positions.
With the marble bags, it seems the author counts all in bag one separate from all in bag two, or bag three. I'm okay with a wrong answer, but asking - given a test environment where I'm not going to be able to ask for any clarification, what in the wording above leads to that conclusion that the bags must be treated differently? Note - had the question said "3 different colored bags", I'd have been satisfied with the answer.
Edit - I've passed the exam. Remarkably, this is the most unsatisfying way I've ever had an exam reported, simply pass/fail. One would think especially for math, that the test taker would like a result with precision, even if it's not offered to prospective employers.