The premise of homogeneous piles is that each item is exactly the same
Upgrade: Put M apples on N plates, and the plates are not allowed to be empty. How many ways are there?
Partition method:
10 apples are the same 4 plates
00/00/0000/00
C93 = 84
C(M-1)(N-1)
Example question: A certain unit allocates 25 excellent employee quotas to 11 departments, and each department has at least 2 quotas. How many different allocation methods are there? B
A.210 B.286 C.315 D.1750
25-11=14 //First assign one person to each department
14 employees --> 11 departments C(14-1)(11-1)=C(13)(10) =286
Example: A certain unit has purchased 9 identical laptop computers and plans to distribute them to 4 different departments. Each department is required to be assigned at least one computer. How many ways are there?
C(9-1)(4-1)=C83=56
Example: A unit has a total of 10 places for further studies allocated to its subordinate departments, and each department has at least one place. If there are 36 different allocation methods, how many departments does the unit have at most?
Example: If a leader wants to assign 20 identical tasks to three subordinates, and each subordinate is assigned at least three tasks, how many different assignment methods are there?
20-2*3=14 //first divide each department into two items
14 tasks --> 3 departments C(13)(2)=78