BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Combinatorics

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Legendary Member
Posts: 504
Joined: Tue Apr 19, 2011 1:40 pm
Thanked: 114 times
Followed by:11 members

Combinatorics

by knight247 » Mon Sep 19, 2011 2:34 am
In how many ways can one choose 6 cards from a normal deck of cards so as to have all suits present?
(A)(13^4) x 48 x 47
(B)(13^4) x 24 x 47
(C)48C6
(D)13^4
(E)(13^4) x 48C6

Slight change made. OA is B
Last edited by knight247 on Mon Sep 19, 2011 7:13 am, edited 2 times in total.
Top
Source: — Problem Solving |
User avatar
Legendary Member
Posts: 1309
Joined: Mon Apr 04, 2011 5:34 am
Location: India
Thanked: 310 times
Followed by:123 members
GMAT Score:750

by cans » Mon Sep 19, 2011 3:41 am
total 52 cards.
select 1 card each from each deck: 13*13*13*13.
now remaining 2 cards can be any. left cards=48. thus 48*47
IMP A
If my post helped you- let me know by pushing the thanks button ;)

Contact me about long distance tutoring!
[email protected]

Cans!!
Top
Legendary Member
Posts: 966
Joined: Sat Jan 02, 2010 8:06 am
Thanked: 230 times
Followed by:21 members

by shankar.ashwin » Mon Sep 19, 2011 3:58 am
I think ordering should not matter for the last 2 cards, so shouldnt it be 48c2? I dont see an option.


cans wrote:total 52 cards.
select 1 card each from each deck: 13*13*13*13.
now remaining 2 cards can be any. left cards=48. thus 48*47
IMP A
Top
Legendary Member
Posts: 966
Joined: Sat Jan 02, 2010 8:06 am
Thanked: 230 times
Followed by:21 members

by shankar.ashwin » Mon Sep 19, 2011 4:01 am
Found this https://www.beatthegmat.com/choose-6-car ... 45411.html
Top
User avatar
Legendary Member
Posts: 504
Joined: Tue Apr 19, 2011 1:40 pm
Thanked: 114 times
Followed by:11 members

by knight247 » Mon Sep 19, 2011 5:07 am
My take
The first card does not matter. We can pick any one of the 52 cards. 52 Ways=13*4
The second card has to be from the remaining 3 decks decks i.e. 39C1= 39 Ways=13*3
The third card has to be from the remaing 2 decks i.e. 26C1=13*2 ways
The fourth card has to be from the last remaining deck i.e. 13C1=13 Ways
The last two can be picked from anyone of the remaining 48 cards i.e. 48C2=48*47/2=24*47 Ways

Multiplying all the ways together
13*4*13*3*13*2*24*47=13^4*24^2*47
Got it...However for the first four cards we have considered ordered sequences hence we need to divide by 4! as order is not important.

13^4*24^2*47/4!=13^4*24*47 Hence B Finally..hehe
Last edited by knight247 on Mon Sep 19, 2011 7:12 am, edited 1 time in total.
Top
User avatar
Master | Next Rank: 500 Posts
Posts: 461
Joined: Tue May 10, 2011 9:09 am
Location: pune
Thanked: 36 times
Followed by:3 members

by amit2k9 » Mon Sep 19, 2011 6:50 am
the first 4 cards are = 13^4
remaining cards = 52-4=48

last two cards will be = 48*47

thus 13^4 * 48*47.

A it is.
For Understanding Sustainability,Green Businesses and Social Entrepreneurship visit -https://aamthoughts.blocked/
(Featured Best Green Site Worldwide-https://bloggers.com/green/popular/page2)
Top
User avatar
Legendary Member
Posts: 504
Joined: Tue Apr 19, 2011 1:40 pm
Thanked: 114 times
Followed by:11 members

by knight247 » Mon Sep 19, 2011 7:44 am
@amit

U've made it into an ordered sequence brother. The answer is B
Top
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Mon Sep 19, 2011 8:25 am
Ignore this problem.
It is far too complex for the GMAT.
Last edited by GMATGuruNY on Fri Nov 20, 2015 6:46 am, edited 1 time in total.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top
User avatar
Legendary Member
Posts: 504
Joined: Tue Apr 19, 2011 1:40 pm
Thanked: 114 times
Followed by:11 members

by knight247 » Fri Oct 07, 2011 11:41 pm
@Mitch
Can u plz confirm if my reasoning is correct! Thanks
Top
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Sat Oct 08, 2011 6:38 am
knight247 wrote:@Mitch
Can u plz confirm if my reasoning is correct! Thanks
As I noted in my post above, I would ignore this problem.
It is far too complex for the GMAT.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top
Post new topic Post Reply
• Page 1 of 1