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A new basketball league is being formed with a team consisting of 3 players. A total of 30 individuals qualify to be on the team. How many teams can be formed?

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Explanation:

this is strangely phrased.

I understand it in the following way (and base my solution on that) :

a new basketball league is being formed with teams consisting of 3 players. a total of 30 individuals qualify to be on a specific team. how many different formations can be formed for this team ?

these are combinations (the order does not matter) without repetition :

30 over 3 (in how many ways can I create groups of 3 out of the 30 individuals).

that means

30! / (3! × (30-3)!) = 30×29×28 / 3! = 30×29×28 / 6 =

= 5×29×28 = 4,060

the order does not matter, because a team formation with the players A, B, C is the same as e.g. C, A, B.

and no repetition, because no individual can be twice or three times in the same team formation. e.g. A, A, A is not a valid team formation.

if my understanding of the question is wrong, please let me know, so that I can correct the solution.

User George Findulov
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