Grouping problem.

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chaitanyareddy: Senior | Next Rank: 100 Posts; Posts: 30; Joined: Fri Feb 27, 2009 12:45 am; Thanked: 1 times; GMAT Score:620

by chaitanyareddy » Mon Aug 16, 2010 6:24 am

Hi Please let me know what is the issue in my approach regarding solving the following problem.

A group of 8 friends want to play doubles tennis. How many different ways can
the group be divided into 4 teams of 2 people?

My approach :

No. of ways for selecting team A : 8C1*7C1.
No. of ways for selecting team B : 6C1*5C1.
No. of ways for selecting team C : 4C1*3C1.
No. of ways for selecting team D : 2C1*1C1.

so total 100.

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Source: Beat The GMAT — Problem Solving | Mon Aug 16, 2010 6:24 am

kmittal82: Master | Next Rank: 500 Posts; Posts: 324; Joined: Mon Jul 05, 2010 6:44 amFollowed by: 3 members; Location: London; Thanked: 70 times

by kmittal82 » Mon Aug 16, 2010 6:42 am

Hi,

Can you please post the OA as well? Sometimes the OA help a great deal in solving the question

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kmittal82: Master | Next Rank: 500 Posts; Posts: 324; Joined: Mon Jul 05, 2010 6:44 amFollowed by: 3 members; Location: London; Thanked: 70 times

by kmittal82 » Mon Aug 16, 2010 6:51 am

chaitanyareddy wrote:Hi Please let me know what is the issue in my approach regarding solving the following problem.

A group of 8 friends want to play doubles tennis. How many different ways can
the group be divided into 4 teams of 2 people?

My approach :

No. of ways for selecting team A : 8C1*7C1.
No. of ways for selecting team B : 6C1*5C1.
No. of ways for selecting team C : 4C1*3C1.
No. of ways for selecting team D : 2C1*1C1.

so total 100.

You have the correct starting point, but what you are missing here is that the order of the people within each team does not matter. Say you have x and y in Team A, using your method xy is not the same as yx.

So, you need to divide each of those by 2 to make the order irrelevant

so, this should give you 8x7/2 x 6x5/2 x 4x3/2 x 2x1/2 = 56/2 x 30/2 x 12/2 x 1 = 28 x 15x6x1 = 28 x 90 number of ways of forming 4 teams of 2 each.

Now, furthermore, the order of the teams themselves shouldn't matter. If your teams are ABCD, then its the same as BCAD etc., so you divide futher by 4!

28 x 90 / 4 x 3 x 2 = 105

Can you check if that is the OA?

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chaitanyareddy: Senior | Next Rank: 100 Posts; Posts: 30; Joined: Fri Feb 27, 2009 12:45 am; Thanked: 1 times; GMAT Score:620

by chaitanyareddy » Mon Aug 16, 2010 9:58 am

OA 105

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crackinggmat: Senior | Next Rank: 100 Posts; Posts: 79; Joined: Thu Jun 03, 2010 11:58 am; Thanked: 1 times

by crackinggmat » Mon Aug 16, 2010 10:44 am

very good explanation kmittal82

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