Your friend has 8 indistinguishable coins. She flips all 8 of them and leaves them face up on the table in front of you. You cannot tell the difference between the different coins or the order in which they were flipped. How many possible different resulting states can there be of the 8 quarters on the
table?
I'm not sure how to approach this problem since the coins are indistinguishable. Do I only consider the possibilities on the flips giving me $2^8$, the ways to arrange them in a row $8!$, or do I have to combine them and consider both?
If the locations are irrelevant, then there are exactly nine states, corresponding to the number of visible heads: $0\ldots 8$.