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Take 9 distinct objects and 5 identical boxes. Exactly one object must be placed into each box. In how many ways can this be done?

According to a similar question, I list 4 cases.

Case 1. $\quad(5,1,1,1,1):$ $\quad^9C_5 = 126$
Case 2. $\quad(4,2,1,1,1):$ $\quad^9C_4 = 126$
Case 3. $\quad(3,3,1,1,1):$ $\quad^9C_3 = 84$
Case 4. $\quad(3,2,2,1,1):$ $\quad^9C_3 = 84$

And then I add them up, but I still get the answer wrong. Can anyone give me some hints on this question?

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Allen_sHH
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    "case1 (5,1,1,1,1) ..." $,$ None of those follow the rule that "*exactly one* object must be placed into each container". – dxiv Jul 24 '22 at 03:23

1 Answers1

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Since the boxes are identical and exactly one object must be placed in each,
simply $\binom95 = 126$ ways

true blue anil
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