How many ways are there to put 4 indistinguishable b***s into 2 distinguishable boxes?
Assuming you can't even tell which box is on the left vs. right as you move the b***s around, and that all b***s must be put into a box...
3
i) You can put all 4 in one, with none in the other
ii) You can move one of those b***s (doesn't matter which one because they're indistinguishable) to the box that's empty in answer i) thus having 3 in one and 1 in the other.
iii) You can move one more to even it out.
... and that's it because as soon as you move another, it's indistinguishable from ii), etc.
5
B***s do not matter but boxes matter
we have following pssible scenarios: 4-0, 0-4, 3-1, 1-3, 2-2
You can consider it like Box A gets 0-4 b***s(5 possibilities) and Box B gets the rest.
Mathemathical explanation may be C(4,2) - 1 (1 for (2,2) scenario which both boxes have same amount and do not have to count the scenario that b***s switch and get (2,2) again)
