Statistics - combinations of subsets

In summary, the Springfield Football Club can make a total of 1,680 teams by choosing 3 forwards out of 8, 4 mid-fielders out of 6, 3 defenders out of 5, and 1 goalkeeper out of 2. This is calculated by using the combination formula of nCr, where n is the total number of players in a position and r is the number of players needed for that position.
  • #1
sara_87
763
0
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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  • #2
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?
 
  • #3
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.
 
  • #4
I was wrong i thought for some reason order mattered when choosing. Sorry
 

Related to Statistics - combinations of subsets

What is the definition of combinations in statistics?

Combinations refer to the different ways in which a subset of a larger set can be selected without taking into account the order in which the elements are chosen.

How is the number of combinations calculated?

The number of combinations can be calculated using the combination formula, which is nCr = n! / r!(n-r)!, where n represents the total number of items in the set and r represents the number of items being chosen in each combination.

What is the difference between combinations and permutations?

Combinations and permutations both involve selecting subsets from a larger set, but permutations take into account the order in which the elements are chosen while combinations do not.

What is the purpose of using combinations in statistics?

Combinations are useful in statistics for determining the probability of a certain outcome in a sample space. They can also be used to calculate the number of possible outcomes in a given situation.

How can combinations be applied in real-life situations?

Combinations can be applied in various real-life situations, such as in genetics to determine the likelihood of certain traits being inherited, in probability to calculate the chances of winning in a game of chance, and in market research to analyze consumer behavior based on different combinations of variables.

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