Last visit was: 25 Apr 2026, 16:53 It is currently 25 Apr 2026, 16:53
Home
Messages
Tests
Schools
Events
Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
User avatar
aiming4mba
User avatar
Joined: 20 Nov 2009
Last visit: 22 May 2012
Posts: 97
Own Kudos:
1,088
 [4]
Given Kudos: 64
Posts: 97
Kudos: 1,088
 [4]
Two distinct packs of 52 playing cards are shuffled together 02 Apr 2010, 10:32
Kudos
Add Kudos
4
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
N
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

(N/A)

Question Stats:

50% (00:42) correct 50% (00:33) wrong based on 6 sessions

History

Date
Time
Result
Not Attempted Yet
Two distinct packs of 52 playing cards are shuffled together. Find the number of ways of selecting 26 cards such that no two cards of the same suit and same denomination are selected? Sorry people, no answer choices available. Only have the solution to this (which I didn't understand).
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 25 Apr 2026
Posts: 109,830
Own Kudos:
811,281
 [1]
Given Kudos: 105,886
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 109,830
Kudos: 811,281
 [1]
Two distinct packs of 52 playing cards are shuffled together 02 Apr 2010, 12:10
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
aiming4mba
Two distinct packs of 52 playing cards are shuffled together. Find the number of ways of selecting 26 cards such that no two cards of the same suit and same denomination are selected? Sorry people, no answer choices available. Only have the solution to this (which I didn't understand).
Show more

104 choices for the first card;
102 choices for the second card, as in 103 cards left (after we chose the first card), there will be 102 different cards from the chosen one;
100 choices for the third card, 102 left and 102-2 are different from two cards already chosen;
...
54 choices for the 26th card.

54*56*...*104 possibilities. BUT we must divide this number by 26! as the order doesn't matter here.

So total # of ways is: \(\frac{54*56*...*104}{26!}=\frac{2^{26}*27*28*...*52}{26!}=\frac{2^{26}*52!}{26!*26!}\)

OR:
If we choose 26 cards from one deck, clearly there won't be two cards of the same suit and same denomination. Now any card chosen can be either from the first deck or from the second, so any card has two options.

Choosing 26 from 52: \(C^{26}_{52}\);
Any card from these 26 has two options 2*2*...*2 - 26 times: \(2^{26}\)

So total # of ways is: \(2^{26}*C^{26}_{52}\) (this is the same as above).

P.S. I doubt this is GMAT question.
User avatar
aiming4mba
User avatar
Joined: 20 Nov 2009
Last visit: 22 May 2012
Posts: 97
Own Kudos:
1,088
Given Kudos: 64
Posts: 97
Kudos: 1,088
Two distinct packs of 52 playing cards are shuffled together 03 Apr 2010, 00:39
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Thanks Bunuel! It makes sense now...
User avatar
hardnstrong
User avatar
Joined: 05 Mar 2010
Last visit: 16 Nov 2015
Posts: 85
Own Kudos:
115
Given Kudos: 8
Posts: 85
Kudos: 115
Two distinct packs of 52 playing cards are shuffled together 04 Apr 2010, 04:49
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
aiming4mba
Two distinct packs of 52 playing cards are shuffled together. Find the number of ways of selecting 26 cards such that no two cards of the same suit and same denomination are selected? Sorry people, no answer choices available. Only have the solution to this (which I didn't understand).

104 choices for the first card;
102 choices for the second card, as in 103 cards left (after we chose the first card), there will be 102 different cards from the chosen one;
100 choices for the third card, 102 left and 102-2 are different from two cards already chosen;
...
54 choices for the 26th card.

54*56*...*104 possibilities. BUT we must divide this number by 26! as the order doesn't matter here.

So total # of ways is: \(\frac{54*56*...*104}{26!}=\frac{2^{26}*27*28*...*52}{26!}=\frac{2^{26}*52!}{26!*26!}\)

OR:
If we choose 26 cards from one deck, clearly there won't be two cards of the same suit and same denomination. Now any card chosen can be either from the first deck or from the second, so any card has two options.

Choosing 26 from 52: \(C^{26}_{52}\);
Any card from these 26 has two options 2*2*...*2 - 26 times: \(2^{26}\)

So total # of ways is: \(2^{26}*C^{26}_{52}\) (this is the same as above).

P.S. I doubt this is GMAT question.
Show more


Bunual dont we divide it by total number of outcomes i.e 104C26
Because probability of anything is - numbers of outcomes of certain thing/total number of outcomes

I am getting confused here. Please explain
User avatar
bnagdev282
User avatar
Joined: 09 Jan 2010
Last visit: 08 Dec 2010
Posts: 17
Own Kudos:
2
Given Kudos: 5
Posts: 17
Kudos: 2
Two distinct packs of 52 playing cards are shuffled together 04 Apr 2010, 13:12
Kudos
Add Kudos
Bookmarks
Bookmark this Post
hardnstring we require the number of possiblities not the probability so we dont need divide by 104c26 hope well its clear now
User avatar
hardnstrong
User avatar
Joined: 05 Mar 2010
Last visit: 16 Nov 2015
Posts: 85
Own Kudos:
115
Given Kudos: 8
Posts: 85
Kudos: 115
Two distinct packs of 52 playing cards are shuffled together 05 Apr 2010, 10:44
Kudos
Add Kudos
Bookmarks
Bookmark this Post
@dev282

silly me again .........i always get confused between probability and combinations
Thanks mate
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,986
Own Kudos:
1,118
Posts: 38,986
Kudos: 1,118
Two distinct packs of 52 playing cards are shuffled together 22 Feb 2025, 13:12
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.
Moderators:
Bunuel
Math Expert
109830 posts
Krunaal
Tuck School Moderator
852 posts