Solving a Combinations Problem: 15 or 21?

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Homework Help Overview

The problem involves determining the number of ways to choose 2 letters from a set of 6 letters (A, B, C, D, E, F) using combinations. The original poster presents a calculation that yields 15, while a drawing suggests a total of 21 combinations, leading to confusion about the correct interpretation of the problem.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to apply the combinations formula but questions the validity of their result when compared to a drawn representation. Some participants question whether letters can be chosen more than once, leading to discussions about the implications of the problem statement.

Discussion Status

Participants are exploring different interpretations of the problem, particularly regarding the allowance of repeated letters in combinations. Guidance has been offered about the importance of clarity in the problem statement and the distinction between combinations and combinations with repetition.

Contextual Notes

There is ambiguity in the problem statement regarding whether letters can be chosen more than once, which affects the interpretation of the combinations involved. This uncertainty is central to the discussion.

christian0710
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Homework Statement



Hi So the problem in combinations is the following: In how many ways can you choose 2 letters from the following 6 letters (A,B,C,D,E,F)

This is a question in combinations so I know the order does not matter, so AB is the same as BA.
I use the equation (n,r) = n!/((n-r)!*r!) = 15 (See my drawing)

The problem is this: If i draw out the possible combinations and add them together i get 21!

What is the correct answer 15 or 21, and why?
 

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You can not choose the same letter twice or can you?

ehild
 
Interesting. Does that mean that in combinations mathematics, you can never use the same 2 letters? Or at least acording the the formulae i use? Ahh so the logic is that you don't have 2 of the same letters in a group of letters, or course :)
Thank you for the hint.
 
christian0710 said:
Interesting. Does that mean that in combinations mathematics, you can never use the same 2 letters? Or at least acording the the formulae i use? Ahh so the logic is that you don't have 2 of the same letters in a group of letters, or course :)
Thank you for the hint.

It means you have to pay attention to the problem statement. Some problems using letters will allow letters to be used more than once, some will not. Problems that draw marbles out of a bag will generally imply that you can't put a marble back after you've used it. And so forth. The problem statement should be clear but in the absence of such clarity it's best to assume things can only be used once. With marbles, that's pretty clear, with letters not so much.
 
If you can choose the same letter again, it is "combination with repetition". The number of possibilities are equal to (n+r-1)/(r! (n-1-r)!). If n=6 and r=2, it is 21.

ehild
 

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