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# Factorial

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Could you let me the possible combinations of the values in the atached sheet pl.?
factorial.xls
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Commented:
If I am understanding what the attached sheet represents, you would just multiply the number of options for each  state

Commented:
Thank you.
Graphics Expert
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Commented:
By analysing State 1, A, B, C, we can have combinations of 2:
AB, BC, AC. <---- 3 combinations
Also   BA, CB, CA     if the order is relevant.   <--- 3 more combinations
Combinations of all of them (permutation):
ABC, ACB, BAC, BCA, CAB, CBA  <--- factorial of 3
How about state 5?? There we have 6!
As it is not defined how many components there are in each combination, we can assume a permutation for each state and, as stated by ozo, just multiply the factorials:
3!    x    3!    x    4!    x    3!    x    6!    x    2!    x    2!     x    1    x    1
Jose

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Commented:
What is the relationship between the attached sheet and the possible combinations?

Graphics Expert
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Commented:
The question doens't define which combination is nor how many elements will be in each combination.
We can combine numbers by adding, multiplying them or just puting them together, so in the representation AB, for instance, we can have a value A + value B, or value A x value B, and so on.
Another interpretation is "how many combinations are there if we use one cell of each column (state)?" For example: AFHKPUVXYZ is one of them. In this case, the combinations are calculated as stated before, just multiplying the number of cells of each state.
Jose
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Commented:
Another interpretation could be how many ways are there of distributing the letters among the columns,
with or without alphabetical constraints, and with or without order being relevant,
that case would not be the same as multiplying the number of options for each state.
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Commented:
That's right. If vignesh_prabhu explain more in detail, we can understand which combinatorics type is looking for: Partitions? Permutations? Combinations? Factorials? Number theory covers a wide field...
As per the question's title, would be about permutations, which uses factorials to calculate it, but I'm not sure of that.
Jose
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