Statistics - combinations of subsets

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Discussion Overview

The discussion revolves around calculating the number of possible teams that can be formed by Springfield Football Club, given specific requirements for player positions and available players. The scope includes combinatorial mathematics and the application of combinations in a sports context.

Discussion Character

  • Mathematical reasoning

Main Points Raised

  • One participant proposes using the formula (8C3) x (6C4) x (5C3) x (2C1) to calculate the number of teams, questioning its correctness.
  • Another participant suggests that when selecting players, the order does not matter, indicating a misunderstanding of the combination concept.
  • A later reply agrees with the initial calculation but expresses confusion about the order of selection.
  • One participant acknowledges a mistake regarding the importance of order in the selection process.

Areas of Agreement / Disagreement

Participants express uncertainty about the correct application of combinations and whether the initial calculation is accurate. There is no consensus on the correct method or final answer.

Contextual Notes

Some participants appear to confuse the concepts of combinations and permutations, leading to differing interpretations of the problem. The discussion does not resolve these misunderstandings.

sara_87
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Springfield Football Club plan to field a team of 3 forwards, 4 mid-fielders and 3 defenders
and a goalkeeper. Assuming they have 8 forwards, 6 mid-fielders, 5 defenders and 2 goal-
keepers on their books how many teams can they make?

i tried doing:
(8C3) x (6C4) x (5C3) x (2C1)
but ithink it's wrong for some reason...is it wrong?
 
Last edited:
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once you choose one person then you can't choose them again...therefore if you were to choose 3 people out of 10...you have 10 to choose from first, then 9 to choose from and 8 for the third choose. Therefore you have 10 x 9 x 8. I hope that's right?
 
sara_87 said:
Springfield Football Club plan to field a team of 3 forwards, 4 mid-fielders and 3 defenders
and a goalkeeper. Assuming they have 8 forwards, 6 mid-fielders, 5 defenders and 2 goal-
keepers on their books how many teams can they make?

i tried doing:
(8C3) x (6C4) x (5C3) x (2C1)
but ithink it's wrong for some reason...is it wrong?
I think you have it right.
 
I was wrong i thought for some reason order mattered when choosing. Sorry
 

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