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permutation or combination or neither ?
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04-07-2015
, 08:00 AM
#1
mstram
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By mstram
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Join Date: Oct 2007
Posts: 239
Given, a 16 bit unsigned integer that contains eight 0 bits, eight 1 bits, how many numeric combinations are there ?
Programmatically I can do it with bit shifting, indexing with where to start the bit shifts.
But is there a combination / permutation / other formula for this particular sequence ?
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04-07-2015
, 08:28 AM
#2
JSLigon
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The number of 16 bit sequences containing exactly eight 1 bits is 16 choose 8, or 16! / (8! * 8!). One of the 8! cancels out giving 16*15*...*9 / 8!
http://en.m.wikipedia.org/wiki/Combination
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04-11-2015
, 09:43 PM
#3
:::grimReaper:::
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Join Date: Jul 2010
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^What he said. If you need the actual bits, use gosper's hack:
http://en.wikipedia.org/wiki/Combina...m#Applications
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