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joeu2004 joeu2004 is offline
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Default A "chessboard" problem

On Dec 26, 10:38*am, "Dana DeLouis" wrote:
With just 22 items being scattered around 64, it sounds to me like the
number of Permutations.

=FACT(64) *- *1.26887E+89


There are "64 choose 22" ways of selecting 22 of the 64 squares on
which to place the pieces. It does not matter whether we choose those
squares in the order of 1,2,...,22 or 22,23,...1, for example. In
Excel, that would be COMBIN(64,22).

If the 22 pieces are distinct (I now believe they are not), there are
FACT(22) ways of ordering the pieces on each of the "64 choose 22"
combinations. You could multiply the two, or you could simply compute
PERMUT(64,22).