cards

Expert replies

shashank.ism: Legendary Member; Posts: 1022; Joined: Mon Jul 20, 2009 11:49 pmFollowed by: 2 members; Location: Gandhinagar; Thanked: 41 times

by shashank.ism » Tue Feb 09, 2010 1:16 pm

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

(13^4) x 48 x 47
(13^4) x 27 x 47
48C6
(13^4)
(13^4) x 48C6

My Websites:
www.mba.webmaggu.com - India's social Network for MBA Aspirants

www.deal.webmaggu.com -India's online discount, coupon, free stuff informer.

www.dictionary.webmaggu.com - A compact free online dictionary with images.

Nothing is Impossible, even Impossible says I'm possible.

Like this post

Source: Beat The GMAT — Problem Solving | Tue Feb 09, 2010 1:16 pm

sanjayism: Junior | Next Rank: 30 Posts; Posts: 26; Joined: Sat Oct 31, 2009 10:52 am; Location: rourkela; Thanked: 1 times

by sanjayism » Wed Feb 10, 2010 10:58 pm

I am confused with answer choices;

answer may be
13^4*48C2

kumar sanjay

Like this post

shashank.ism: Legendary Member; Posts: 1022; Joined: Mon Jul 20, 2009 11:49 pmFollowed by: 2 members; Location: Gandhinagar; Thanked: 41 times

by shashank.ism » Wed Feb 10, 2010 11:13 pm

sanjayism wrote:I am confused with answer choices;

answer may be
13^4*48C2

52 cards in a deck -13 cards per suit
First card - let us say from suit hearts = 13C1 =13
Second card - let us say from suit diamonds = 13C1 =13
Third card - let us say from suit spade = 13C1 =13
Fourth card - let us say from suit clubs = 13C1 =13
Remaining cards in the deck= 52 -4 = 48
Fifth card - any card in the deck = 48C1
Sixth card - any card in the deck = 47C1
Total number of ways = 13 * 13 * 13 * 13 * 48 * 47 = 134 *48*47

so ANS is A

Like this post

GMAT/MBA Expert

Ian Stewart: GMAT Instructor; Posts: 2623; Joined: Mon Jun 02, 2008 3:17 amFollowed by: 355 members; Location: Montreal; Thanked: 1090 times; GMAT Score:780

by Ian Stewart » Thu Feb 11, 2010 12:22 am

I'm not sure where this question is from, but it has been posted on this forum before, and it is a mess; none of the answer choices are correct. It is a much harder question than it may appear at first (and is *way* out of scope for the GMAT), and most of the 'solutions' I've seen posted to it, including the one above, dramatically overcount the number of possibilities. In another thread, Brent Hanneson has given an excellent explanation of this:

www.beatthegmat.com/choose-6-cards-from ... 45411.html

For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

ianstewartgmat.com

Like this post

shashank.ism: Legendary Member; Posts: 1022; Joined: Mon Jul 20, 2009 11:49 pmFollowed by: 2 members; Location: Gandhinagar; Thanked: 41 times

by shashank.ism » Thu Feb 11, 2010 1:25 am

Ian Stewart wrote:I'm not sure where this question is from, but it has been posted on this forum before, and it is a mess; none of the answer choices are correct. It is a much harder question than it may appear at first (and is *way* out of scope for the GMAT), and most of the 'solutions' I've seen posted to it, including the one above, dramatically overcount the number of possibilities. In another thread, Brent Hanneson has given an excellent explanation of this:

www.beatthegmat.com/choose-6-cards-from ... 45411.html

Thanks Ian, Brent has given very good explanation of the question.

Like this post

komal: Legendary Member; Posts: 777; Joined: Fri Jan 01, 2010 4:02 amFollowed by: 47 members; Location: Mumbai, India; Thanked: 117 times

by komal » Tue Feb 16, 2010 10:32 am

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

(13^4) x 48 x 47
(13^4) x 27 x 47
48C6
(13^4)
(13^4) x 48C6

4 cards from 4 suits = 13^4

Now the 5th card can be drawn in 48 ways and the 6th one in 47 ways

So the number of ways = 13^4 * 48 * 47

(A) is correct

https://www.e-gmat.com/

Like this post

GMAT/MBA Expert

Ian Stewart: GMAT Instructor; Posts: 2623; Joined: Mon Jun 02, 2008 3:17 amFollowed by: 355 members; Location: Montreal; Thanked: 1090 times; GMAT Score:780

by Ian Stewart » Tue Feb 16, 2010 12:11 pm

komal wrote:
shashank.ism wrote:In how many ways can one choose 6 cards from a normal deck of cards so as to have all suits present?

(13^4) x 48 x 47
(13^4) x 27 x 47
48C6
(13^4)
(13^4) x 48C6
4 cards from 4 suits = 13^4

Now the 5th card can be drawn in 48 ways and the 6th one in 47 ways

So the number of ways = 13^4 * 48 * 47

(A) is correct

That is the solution I've seen posted in several threads in response to this question, and it is not correct, though it may appear to be at first. There are several problems with it:

* your first four cards do not need to be of different suits. We could pick, for example, three Spades first, then a Club, Heart and Diamond, and end up with all four suits

* the order of the selection does not matter here; that needs to be accounted for. Otherwise you are counting the same selections multiple times. See Brent's explanation at the link I posted above.

The correct answer to this question is not among the answer choices provided, and in any case, it is well beyond the scope of the GMAT.

For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

ianstewartgmat.com

Like this post

jeffedwards: Master | Next Rank: 500 Posts; Posts: 109; Joined: Mon Oct 12, 2009 4:58 amFollowed by: 1 member; Thanked: 12 times; GMAT Score:720

by jeffedwards » Tue Feb 16, 2010 12:17 pm

I agree, I got A[/b]

Like this post

komal: Legendary Member; Posts: 777; Joined: Fri Jan 01, 2010 4:02 amFollowed by: 47 members; Location: Mumbai, India; Thanked: 117 times

by komal » Tue Feb 16, 2010 7:14 pm

Ian Stewart wrote:
That is the solution I've seen posted in several threads in response to this question, and it is not correct, though it may appear to be at first. There are several problems with it:

* your first four cards do not need to be of different suits. We could pick, for example, three Spades first, then a Club, Heart and Diamond, and end up with all four suits

* the order of the selection does not matter here; that needs to be accounted for. Otherwise you are counting the same selections multiple times. See Brent's explanation at the link I posted above.

The correct answer to this question is not among the answer choices provided, and in any case, it is well beyond the scope of the GMAT.

Yes i learnt this method from one of ur posts. Dint find any problem with it until u mentioned it above. Thank you very much.

https://www.e-gmat.com/

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

560 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review