Total number of different combination

In summary, the total number of permutations for a four-digit number with all different digits is 24, but if one digit is repeated, the total permutations would be divided by the factorial of the number of repeated digits. For example, if the number is 1966, the total permutations would be 12. However, if there are three or more repeated digits, the calculation would be different.
  • #1
msa969
3
0
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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  • #2
Are you asking about "permutations" or "combinations"?
 
  • #3
so if I had the number 4573 what would be the total permutations?
and similarly 1966 total permutations
 
  • #4
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.
 
  • #5
colours makes perfect sense
 
  • #6
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.
 

1. What does the term "total number of different combinations" mean?

The total number of different combinations refers to the number of unique ways that a set of items can be arranged or combined. This can include permutations, where the order of the items matters, or combinations, where the order does not matter.

2. How do you calculate the total number of different combinations?

To calculate the total number of different combinations, you can use the formula nCr = n! / (r!(n-r)!), where n represents the total number of items and r represents the number of items chosen for each combination. Alternatively, you can use a combination calculator or manually list out all possible combinations and count them.

3. Can the total number of different combinations be infinite?

No, the total number of different combinations is always a finite number. Even if the number is very large, it is still a specific and countable value.

4. How is the total number of different combinations useful in science?

The total number of different combinations is useful in science for analyzing data and determining the possible outcomes of experiments. It can also be used in statistics and probability to calculate the likelihood of certain events occurring.

5. Are there any other factors that can affect the total number of different combinations?

Yes, there are other factors that can affect the total number of different combinations, such as restrictions on the items being combined (e.g. only using a certain number of each item) or repetition of items (e.g. being able to use the same item multiple times in a combination). These factors may require different formulas or methods to calculate the total number of combinations.

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