Total number of different combination

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Discussion Overview

The discussion revolves around calculating the total number of different combinations or permutations of a set of numbers, particularly when some numbers are repeated. Participants explore the implications of having identical numbers in the set and how that affects the total count.

Discussion Character

  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant calculates the total permutations for four distinct numbers as 24.
  • Another participant questions whether the discussion is about "permutations" or "combinations."
  • A participant asks for the total permutations of the number 4573, reiterating the earlier calculation of 24.
  • For the number 1966, one participant suggests the total permutations are 12, explaining the need to account for overcounting due to the repeated digit.
  • Another participant agrees with the need to account for overcounting but emphasizes that the division should be by 2 factorial, highlighting that the approach changes if more than two digits are the same.

Areas of Agreement / Disagreement

Participants express differing views on the correct method for calculating permutations when identical numbers are present, indicating that the discussion remains unresolved regarding the best approach.

Contextual Notes

There are assumptions about the treatment of repeated digits and the implications for counting permutations, which are not fully resolved. The discussion does not clarify how to handle cases with three or more identical digits.

msa969
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I know that if you have 4 numbers eg. 1,23,4 then the total number fo diffferent combination is
4*3*2*1 = 24
what about if one number is the same eg. 1966

Thank you
 
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Are you asking about "permutations" or "combinations"?
 
so if I had the number 4573 what would be the total permutations?
and similarly 1966 total permutations
 
msa969 said:
so if I had the number 4573 what would be the total permutations?
24, as you calculated.

msa969 said:
and similarly 1966 total permutations
12. Imagine that the two sixes are different (e.g., different colors). You start by counting 4x3x2x1, but that means that you have overcounted because 6169 is the same as 6169. You then simply divide by two to remove the overcounting: 4! / 2 = 12.
 
colours makes perfect sense
 
I believe you need to divide by 2 factorial, NOT 2.
Yes it is the same in this problem
But not if 3 or more are the same.
 

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