Possible number of combinations.

In summary, the possible number of combinations for rearranging n objects is n!, but if one object cannot be placed in a specific spot, the number decreases to (n-1)! and if multiple objects cannot be placed in specific spots, the number decreases further.
  • #1
dE_logics
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I just wanted to confirm this...suppose we need to rearrange n number of objects, the possible ways they can be rearranged is n!

If suppose at the first place, one of the objects cannot be admitted...then it will be (n-1)*(n-1)*(n-2)*(n-3)...right?

Instead of the first place, suppose, an object cannot be admitted to any other place...it won't make any difference right?...I mean, the total combinations will still be (n-1)*(n-1)*(n-2)*(n-3)?

Also related to the above question, if we have n 'types' of objects infinite in quantity (actually it's more of permutation) and one of them cannot be admitted to a place (not necessarily the first)...then the possible number of combinations will be (n-1)*n*n*n...etc...right? Also in case of multiple exceptions for instance object 'x' cannot be admitted to first, second and third place or object 'x' cannot be admitted to first, object 'y' cannot be admitted to second and finally object 'z' cannot be admitted to the third place, then will the possible combinations will be (n-1)*(n-1)*(n-1)*n*n*n... etc ?
 
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  • #2
Is it that no one is understanding the question?
 
  • #3
dE_logics said:
I just wanted to confirm this...suppose we need to rearrange n number of objects, the possible ways they can be rearranged is n!

If suppose at the first place, one of the objects cannot be admitted...then it will be (n-1)*(n-1)*(n-2)*(n-3)...right?
Yes. The total number of combinations without the constraint is n!. The constraint removes (n-1)! combinations so the total number is:
n! - (n-1)! = n*(n-1)! - (n-1)! = (n-1)(n-1)! = (n-1)(n-1)(n-2)...*2*1
Instead of the first place, suppose, an object cannot be admitted to any other place...it won't make any difference right?...I mean, the total combinations will still be (n-1)*(n-1)*(n-2)*(n-3)?
How could it matter?

Also related to the above question, if we have n 'types' of objects infinite in quantity (actually it's more of permutation) and one of them cannot be admitted to a place (not necessarily the first)...then the possible number of combinations will be (n-1)*n*n*n...etc...right? Also in case of multiple exceptions for instance object 'x' cannot be admitted to first, second and third place or object 'x' cannot be admitted to first, object 'y' cannot be admitted to second and finally object 'z' cannot be admitted to the third place, then will the possible combinations will be (n-1)*(n-1)*(n-1)*n*n*n... etc ?
correct
 
Last edited:
  • #4
n! - (n-1)! = n*(n-1)! - (n-1)! = (n-1)(n-1)! = (n-1)(n-1)(n-2)...*2*1

So I'm right?

How could it matter?

Ok, thanks.

correct

Again...thanks.
 

Related to Possible number of combinations.

1. How do you calculate the possible number of combinations?

To calculate the possible number of 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 you are selecting from the total.

2. What is the difference between permutations and combinations?

The main difference between permutations and combinations is that in permutations, the order of the items matters, whereas in combinations, the order does not matter. Additionally, in permutations, each item can only be used once, whereas in combinations, items can be repeated.

3. Can the possible number of combinations ever be larger than the total number of items?

No, the possible number of combinations can never be larger than the total number of items. This is because each combination is made up of a subset of the total items, and the total number of combinations cannot exceed the total number of items.

4. How is the possible number of combinations useful in real-world applications?

The possible number of combinations is useful in fields such as mathematics, statistics, and computer science. It can be used to calculate probabilities, create algorithms, and analyze data. It also has practical applications in fields such as genetics, where it can be used to analyze and predict genetic combinations.

5. Are there any limitations to the possible number of combinations formula?

Yes, the possible number of combinations formula assumes that all items are distinct and that each item can only be used once. If these assumptions do not hold, then the formula may not accurately calculate the possible number of combinations. Additionally, the formula does not take into account any external factors or constraints that may limit the actual number of combinations in a real-world scenario.

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