AMC 10 Weekly Practice Round 3
Complete problem set with solutions and individual problem pages
A science and technology expo is held in a certain place with exhibition halls. There are volunteer slots to be assigned to these halls, with the requirements that each hall receives at least one slot and the numbers of slots assigned to the halls are all different. How many different assignment methods are there?
- A.
- B.
- C.
- D.
- E.
“The distribution method in which each hall receives at least one slot” is equivalent to choosing two gaps from the gaps between the slots to insert dividers, which gives
methods.
The distributions in which at least two halls receive the same number of slots are
for a total of
cases.
Therefore, the number of distributions in which each hall receives at least one slot and all halls receive different numbers of slots is
Thus, the answer is .
