Determine the number of its n-combinations

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In summary, the number of n-combinations can be determined using the formula n! / (r! * (n-r)!), where n is the total number of items and r is the number of items being chosen. The "n" in n-combinations represents the total number of items or elements available to choose from. An example of determining n-combinations is finding the number of 3-letter combinations from a set of 5 letters (A, B, C, D, E). Determining n-combinations is useful in various situations, such as selecting a team, creating a password, or calculating possible outcomes. Another method for determining n-combinations is by using a combination table or chart.
  • #1
Jrb599
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Consider the multiset {n*a, n*b, 1, 2 , 3,..., n+1} of size 3n + 1. Determine the number of its n-combinations.

I'm stuck on this one, any help would great.
 
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  • #2
How is its size 3n+1 and not n+3?
 
  • #3
Consider the case n=2

you get

(a,a,b,b 1,2,3) which gives you 7 elements

not 5, so 3n + 1 holds.
 
  • #4
PRoblem solved, will this thread be deleted?
 

1. How do you determine the number of n-combinations?

The number of n-combinations can be determined by using the formula n! / (r! * (n-r)!), where n is the total number of items and r is the number of items being chosen.

2. What does the "n" in n-combinations represent?

The "n" in n-combinations represents the total number of items or elements that are available to choose from.

3. Can you give an example of determining n-combinations?

Sure, let's say we have a set of 5 letters (A, B, C, D, E) and we want to find the number of 3-letter combinations. Using the formula, we would have n = 5 and r = 3, so the number of n-combinations would be 5! / (3! * (5-3)!) = 10.

4. How is determining n-combinations useful in real life?

Determining n-combinations is useful in many applications, such as choosing a team from a group of people, creating a password with a certain number of characters, or calculating the number of possible outcomes in a game or experiment.

5. Are there any other methods for determining n-combinations?

Yes, another method for determining n-combinations is by using a combination table or chart, which lists all the possible combinations for a given n and r. This method can be helpful for larger numbers or when the formula may be difficult to use.

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