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Title [Harim Yoo] AMC question
AMC 1012 must know concept 03 03
Author cut*** Date Posted 2024-03-10 오후 8:10:46
Why can't we do 5!/4!2! in this case? The answer says its 3. But if numbers were bigger, would we just have to use casework? Or is there a formula that we can use other than the one I wrote above? I don't get why 5! (total ways to place marbles) /4! (Same color) 2! (Same color) wouldn't work.
Attachment Screenshot2024-03-10at8.06.40PM.png
Attachment Screenshot2024-03-10at8.10.22PM.png
2024-03-11 오전 11:23:20

Great question!

 

5!/4!2! already implies that 6 objects are all different. In this setup, 6 objects are not all distinguishable.

Hence you always perform casework, and because there is no easy way out, it is likely to come out in mid 10s in AMC or equivalent exams!

 

Hope this helps!

 

 
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