How do you know if a Q is asking for an ordered subgroups

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athary: Newbie | Next Rank: 10 Posts; Posts: 3; Joined: Tue Apr 03, 2012 2:18 pm

by athary » Wed Apr 11, 2012 12:20 am

A certain company will issue 4-letter identification codes to all of its employees. The codes will include only the letters A, C, F, H, K, Q and V. If all the letters of each code are distinct, how many such codes are possible?

The correct answer is 840. This question is asking for the number of ordered subgroups we can make out of a larger group. The permutation formula for ordered subgroups

How do you know if a Q is asking for an ordered subgroups??

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Source: Beat The GMAT — Problem Solving | Wed Apr 11, 2012 12:20 am

Pharo: Senior | Next Rank: 100 Posts; Posts: 61; Joined: Mon Jan 18, 2010 11:09 pm; Thanked: 8 times

by Pharo » Wed Apr 11, 2012 12:38 am

An identification code should be unique; so the order of the letters matter. In addition, the letters in the code should be unique in other words should appear only once.

Do not look at it as "groups vs sub groups". Check if the order and repetition matter or not

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Shalabh's Quants: Master | Next Rank: 500 Posts; Posts: 134; Joined: Fri Apr 06, 2012 3:11 amFollowed by: 5 members; Thanked: 35 times

by Shalabh's Quants » Wed Apr 11, 2012 3:59 am

athary wrote:A certain company will issue 4-letter identification codes to all of its employees. The codes will include only the letters A, C, F, H, K, Q and V. If all the letters of each code are distinct, how many such codes are possible?

The correct answer is 840. This question is asking for the number of ordered subgroups we can make out of a larger group. The permutation formula for ordered subgroups

How do you know if a Q is asking for an ordered subgroups??

I think I understand your problem. You mean when to apply Permutation and when Combination?

Thumb Rule-- Whenever Qn. uses words like Arrangement, Distinct, Unique. One must calculate Permutation & when Qn. uses words like Selection, Choose, calculate combination.

In this question, a Code say ACFH will be different than AFCH, hence use permutation only, as arrangement matters.

Shalabh Jain,
e-GMAT Instructor

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athary: Newbie | Next Rank: 10 Posts; Posts: 3; Joined: Tue Apr 03, 2012 2:18 pm

by athary » Wed Apr 11, 2012 8:31 am

thanks that really helps!!!

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