To anyone who could help clarify something for me:
I approached this question in the following way:
Assuming that each letter is represent by L => 5 letters = L L L L L
and
Assuming each letter box is separated by *
One way of posting 5 letters into 4 letter boxes could be represented by LL*L*L*L (2,1,1,1) or LLLL* * *L (4,0,0,1) or L*LL*LL* (1,2,2,0)
Since there are 5 identical L's and 3 identical *'s,
there are 8!/(5!3!) ways = 56 ways to post 5 letters into 4 letter boxes.
Why is this calculation different from the OA of 4^5?
Is it because in Brent's answer, it is assumed that each letter is NOT identical and each letter box is also NOT identical?
If so, what is a general rule to calculate how many ways to distribute N objects into X bins for when:
i. N objects are distinct and X bins are distinct
ii. N objects are identical and X bins are identical
iii. N objects are distinct and X bins are identical
iv. N objects are identical and X bins are distinct
?
Sorry for the long question but I have been trying to wrap my brain around this but to no avail.
Please help!
