An apartment block has $8$ tenants, each with a separate mail slot. Twelve different pieces of junk mail are delivered.
$(a)$ In how many ways can the mail be delivered if two tenants get three pieces of junk mail and six get one piece?
$(b)$ In how many ways can the mail be delivered if the only restriction is that every tenant gets at least one piece of mail?
I am super confused on where to start with this question. For a, I tried $(8!/3!3!)$ which gave me $1120$ combinations, but that did not seem right. I also tried doing ($^8C_3)*(6!)$ which gave me $40320$ combinations.
I'd appreciate any help!
EDIT
I think I managed A, thank you guys. I'm now just stuck on part B of the questions. I feel like I'm just missing something super simple
(a) Number of ways to distribute different junk mails $ = \displaystyle {12 \choose 3} \cdot {9 \choose 3} \cdot 6!$
Explanation: choose $3$ junk mails for one of the two tenants who receive three junk mails each. Then choose $3$ from remaining $9$ for the other. Rest $6$ mails can be distributed to each of them in $6!$ ways.
If these $2$ tenants can be any two of them out of eight, then multiply the result by $ \ \displaystyle {8 \choose 2}$
b) Hint: Use Principle of Inclusion Exclusion or Stirling Number of the second kind. Using Stirling Number of the second kind (wiki)