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probabiblity combinations

 
 
Mzansi
 
Reply Mon 1 Jul, 2019 06:43 am
Hello. I would like to find out how to calculate the number of possible samples I can get when the sample number is bigger than the range? i.e. the range has three numbers and a sample must have 5 numbers. The numbers in the range can be repeated and a sample can either have only one of the numbers in the range or a combination of two or three of the numbers in the range. I know how to do this 'manually' I am just looking for a formula I can use to do this?
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Type: Question • Score: 0 • Views: 267 • Replies: 3
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engineer
 
  1  
Reply Mon 1 Jul, 2019 08:55 am
@Mzansi,
Could you give me an example of what you are looking for? For example, are you saying the range is {1,2,3} and you are trying to make five number combinations from that like { 1,2,3,2,3} ?
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nacredambition
 
  1  
Reply Mon 1 Jul, 2019 07:15 pm
@Mzansi,
Quote:
a sample can either have only one of the numbers in the range or a combination of two or three of the numbers in the range


Therefore each sample of five numbers has at least one of each number and no more than three.

There are 3 ways of choosing the first number, three ways of choosing the second number, three ways of choosing the third number, two ways of choosing the fourth number and only one way of choosing the final number.

3 x 3 x 3 x 2 x 1
engineer
 
  1  
Reply Mon 1 Jul, 2019 07:29 pm
@nacredambition,
That approach targets permutations. There are only six combinations in that scenario.

1 1 1 2 3
2 2 2 1 3
3 3 3 1 2
1 1 2 2 3
1 1 2 3 3
1 2 2 3 3

I think the answer is n(m-n) where n is the number of choice and m is the number of slots to put them in, but I haven't rigorously tested that answer.
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