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# How many different ways can two basketball teams be formed from 7 frie

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Math Expert
Joined: 02 Sep 2009
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How many different ways can two basketball teams be formed from 7 frie  [#permalink]

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27 Dec 2016, 09:07
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Difficulty:

5% (low)

Question Stats:

85% (00:51) correct 15% (00:49) wrong based on 201 sessions

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How many different ways can two basketball teams be formed from 7 friends?

(1) Any combination of players is allowable except those with one or two members.
(2) All teams must have at least 3 players.

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Re: How many different ways can two basketball teams be formed from 7 frie  [#permalink]

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27 Dec 2016, 10:34
Bunuel wrote:
How many different ways can two basketball teams be formed from 7 friends?

(1) Any combination of players is allowable except those with one or two members.
(2) All teams must have at least 3 players.

I’ll start from the second one.

(2) All teams must have at least 3 players

The only way we can actually divide 7 players into groups with at least 3 players is when one group will consist of 3 players and another one from 4. We can’t make team from one left player so he/she should be added to one of the 3-player teams.

$$\frac{7!}{4!3!}$$ Sufficient.

(1) Any combination of players is allowable except those with one or two members.

This is another way to say that team should consist of at least 3 players. Sufficient.

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Re: How many different ways can two basketball teams be formed from 7 frie  [#permalink]

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27 Dec 2016, 23:33
2
Ans D.
Each of the conditions is asking for ways in which two teams can be formed from 7 friends with a constraint that each team should have at least 3 members.
Hence, both condition 1 and 2 are individually sufficient.
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Re: How many different ways can two basketball teams be formed from 7 frie  [#permalink]

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01 Nov 2018, 04:15
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Re: How many different ways can two basketball teams be formed from 7 frie   [#permalink] 01 Nov 2018, 04:15
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