If I have 12 objects and three jars, how many ways are there to arrange these 12 objects into 3 groups of 4 each? I assume that if I label the objects 1,2,3,4 then it equals 4,3,2,1 etc, meaning I don't care about sequence. Is this just 12 choose 3? Thanks
[Math] How many ways are there to arrange 12 objects into 3 groups of four objects each
combinatorics
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Best Answer
The answer is $12 \choose 4$ $8 \choose 4$. The first factor represents the number of ways to select 4 objects out of the 12 to create the first group. The second factor is the number of ways to create the second group. There is no third factor since the remaining objects are all in the third group (although you could multiply with $4 \choose 4$, which equals 1).