Let me explain by example.
Q: Given four possible values, {1,2,3,4}
, how many 2 value permutations are there ?
A: 16.
(1,1), (1,2), (1,3), (1,4)
(2,1), (2,2), (2,3), (2,4)
(3,1), (3,2), (3,3), (3,4)
(4,1), (4,2), (4,3), (4,4)
However, running 4P2
through Wolfram Alpha gives me an answer of 12
.
Q: Similarly, given four possible values, {1,2,3,4}
, how many 2 value combinations are there?
A: 10.
(1,1), (1,2), (1,3), (1,4)
(2,2), (2,3), (2,4)
(3,3), (3,4)
(4,4)
However, running 4C2
through Wolfram Alpha gives me an answer of 6
.
I'm assuming because the implementations of nCm
and nPm
removed the element from the source set so it can't be chosen again. (similar to lottery balls picked from a drum).
Is there other terminology/formulae for the equivalent where it's possible to return each value. The real life situation would be dice-rolls, where all 6 options are still available on each subsequent roll of the dice.
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