combination and permutation

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opponent: Junior | Next Rank: 30 Posts; Posts: 10; Joined: Thu Feb 17, 2011 3:44 amFollowed by: 1 member

by opponent » Thu Mar 03, 2011 9:46 am

In how many ways can one choose 6 cards from a normal deck of cards so as to have all suits present

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Source: Beat The GMAT — Problem Solving | Thu Mar 03, 2011 9:46 am

Night reader: Legendary Member; Posts: 1337; Joined: Sat Dec 27, 2008 6:29 pmFollowed by: 10 members; Thanked: 127 times

by Night reader » Thu Mar 03, 2011 10:28 am

this problem is missing regular definitions:
the number of suits
the number of cards of the same suit

further it can be deduced the number of cards in a deck

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opponent wrote:In how many ways can one choose 6 cards from a normal deck of cards so as to have all suits present

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Rich@VeritasPrep: GMAT Instructor; Posts: 147; Joined: Tue Aug 25, 2009 7:57 pmFollowed by: 17 members; Location: New York City; Thanked: 76 times; GMAT Score:770

by Rich@VeritasPrep » Thu Mar 03, 2011 12:50 pm

This is a question that has been bounced around on many MANY forums. It's not a very GMAT-like question, because its language is not precise enough.

The biggest problem I see with the question is that it is unclear whether order matters.

"How many ways" could involve distinct arrangements (i.e. permutations) or merely groups (i.e. combinations). Each situation will yield a different answer.

The good news is that the GMAT is very specific in its use of language. If you see a question with words like "distinct arrangements" or "orderings", you know it must involve permutations. If you see a word like "group", you know that order does not matter, and thus combinations are used.

Rich Zwelling
GMAT Instructor, Veritas Prep

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