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 Post subject: permutation and combinationPosted: Fri, 27 Apr 2012 17:25:51 UTC
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Joined: Wed, 15 Feb 2012 07:19:33 UTC
Posts: 31
A judo club has 10 members, of whom 2 are heavy weight players, 5 are middle weight players and 3 are light weight players. The club wants to send a team of 7 players to participate in a competition. The team must consist of a heavy weight player, 2 middle weight players, and 2 reserves from any weight category.

Find the number of ways in which the team can be selected.

My answer is simply 2C1 x 5C2 x 7C4 (remaining 4 players inclusive of reserves) = 420, but the answer given is 600. I'm not sure if it's something in the phrasing of the question i missed out, can anyone explain why? thanks!

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 Post subject: Re: permutation and combinationPosted: Fri, 27 Apr 2012 18:17:04 UTC
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Joined: Tue, 16 Aug 2011 23:38:56 UTC
Posts: 124
thesocialnetwork wrote:
A judo club has 10 members, of whom 2 are heavy weight players, 5 are middle weight players and 3 are light weight players. The club wants to send a team of 7 players to participate in a competition. The team must consist of a heavy weight player, 2 middle weight players, and 2 reserves from any weight category.

Find the number of ways in which the team can be selected.

My answer is simply 2C1 x 5C2 x 7C4 (remaining 4 players inclusive of reserves) = 420, but the answer given is 600. I'm not sure if it's something in the phrasing of the question i missed out, can anyone explain why? thanks!

On the above sentence 2 light weight players is missing.

The correct sentence is:
The team must consist of a heavy weight player, 2 middle weight players, 2 light weight players and 2 reserves from any weight category.

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 Post subject: Re: permutation and combinationPosted: Sat, 28 Apr 2012 02:26:32 UTC
 Member of the 'S.O.S. Math' Hall of Fame

Joined: Mon, 19 May 2003 19:55:19 UTC
Posts: 8107
Location: Lexington, MA
Hello, thesocialnetwork!

You have a typo in the problem . . .
And I don't agree with their answer either.

Quote:
A judo club has 10 members of whom 2 are heavyweights, 5 are middleweights and 3 are lightweights.

The club wants to send a team of 7 players to participate in a competition.
The team must consist of 1 heavyweight, 2 middleweight players, and 4 reserves from any weight category

Find the number of ways in which the team can be selected.

My answer is simply . This is incorrect.
. . but the answer given is 600.

. .

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 Post subject: Re: permutation and combinationPosted: Sat, 28 Apr 2012 06:09:13 UTC
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Joined: Mon, 29 Dec 2008 17:49:32 UTC
Posts: 6782
Location: On this day Taiwan becomes another Tiananmen under Dictator Ma.
thesocialnetwork wrote:
A judo club has 10 members, of whom 2 are heavy weight players, 5 are middle weight players and 3 are light weight players. The club wants to send a team of 7 players to participate in a competition. The team must consist of a heavy weight player, 2 middle weight players, and 2 reserves from any weight category.

Find the number of ways in which the team can be selected.

My answer is simply 2C1 x 5C2 x 7C4 (remaining 4 players inclusive of reserves) = 420, but the answer given is 600. I'm not sure if it's something in the phrasing of the question i missed out, can anyone explain why? thanks!

Let's go by fam's interpretation.

If you have to name your reserves, then it is

On the other hand, if you don't have to name the reserves, then your team could have (heavy,middle,light) = (1,3,3), (2,2,3),(2,3,2), or (1,4,2). So there are

_________________

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 Post subject: Re: permutation and combinationPosted: Sat, 28 Apr 2012 06:23:18 UTC
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Joined: Wed, 15 Feb 2012 07:19:33 UTC
Posts: 31
thanks for all the help! it's appreciated.

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