chesstitans wrote:
help,
VeritasPrepKarishmawhy the formula (ax)! / a! (x!)^a does not work?
Note that you are distributing 16 gifts among 4 children. The children are distinct. If you were distributing the gifts among 4 identical baskets such that each basket has exactly 4 gifts, then you would need to divide by 4! too.
Note where this formula comes from:
Put all 16 gifts in a row in 16! ways.
G1, G2, G3, G4, ... , G16
Now split them into 4 groups
G1, G2, G3, G4 || G5, G6, G7, G8 || ... || G13, G14, G15, G16
If the 4 groups are identical (like identical baskets), divide by 4!
16!/4!
Now since we don't want to arrange the gifts within the group, divide by 4! four times
16!/4!*(4!)^4
But since we have 4 distinct children here, we will not divide by the first 4!
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