• Free Veritas GMAT Class
Experience Lesson 1 Live Free

Available with Beat the GMAT members only code

• Free Trial & Practice Exam
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• 1 Hour Free
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• Award-winning private GMAT tutoring
Register now and save up to \$200

Available with Beat the GMAT members only code

• Get 300+ Practice Questions

Available with Beat the GMAT members only code

• 5-Day Free Trial
5-day free, full-access trial TTP Quant

Available with Beat the GMAT members only code

• Free Practice Test & Review
How would you score if you took the GMAT

Available with Beat the GMAT members only code

• Magoosh
Study with Magoosh GMAT prep

Available with Beat the GMAT members only code

• 5 Day FREE Trial
Study Smarter, Not Harder

Available with Beat the GMAT members only code

## Difficult Math Question #20 - Combinations

This topic has 5 member replies
800guy Master | Next Rank: 500 Posts
Joined
27 Jun 2006
Posted:
354 messages
Followed by:
5 members
11

#### Difficult Math Question #20 - Combinations

Fri Sep 22, 2006 10:04 am
OA coming after some people answer..

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 27 x 47
c. 48C6
d. 13^4
e. (13^4) x 48C6

Need free GMAT or MBA advice from an expert? Register for Beat The GMAT now and post your question in these forums!
gamemaster Senior | Next Rank: 100 Posts
Joined
03 Sep 2006
Posted:
34 messages
Thu Oct 05, 2006 12:13 am
but arent you repeating on options like this?

this is what's confusing, i dont think you can just multiply (13^4) by 48*47

lets take 1,2,3 of type hart and 4,5,6 of 3 different types, so:

{1,4,5,6} {2,3}
{2,4,5,6} {1,3}
{3,4,5,6} {2,1}

are the same choises, you have here a very large number of repetitions

please elaborate on this if you understand what i mean

Thanks

gamemaster Senior | Next Rank: 100 Posts
Joined
03 Sep 2006
Posted:
34 messages
Thu Oct 05, 2006 12:16 am
i think i got it ...

the solution applies only for cases where the order of picking matters, so in this case:

{1,2,3,4} {5,6}

is different than

{2,2,3,4} {3,1}

This should be clarified in the question!, otherwise the solution should be different ... (i think )

gamemaster Senior | Next Rank: 100 Posts
Joined
03 Sep 2006
Posted:
34 messages
Thu Oct 05, 2006 12:13 am
but arent you repeating on options like this?

this is what's confusing, i dont think you can just multiply (13^4) by 48*47

lets take 1,2,3 of type hart and 4,5,6 of 3 different types, so:

{1,4,5,6} {2,3}
{2,4,5,6} {1,3}
{3,4,5,6} {2,1}

are the same choises, you have here a very large number of repetitions

please elaborate on this if you understand what i mean

Thanks

gamemaster Senior | Next Rank: 100 Posts
Joined
03 Sep 2006
Posted:
34 messages
Thu Oct 05, 2006 12:16 am
i think i got it ...

the solution applies only for cases where the order of picking matters, so in this case:

{1,2,3,4} {5,6}

is different than

{2,2,3,4} {3,1}

This should be clarified in the question!, otherwise the solution should be different ... (i think )

800guy Master | Next Rank: 500 Posts
Joined
27 Jun 2006
Posted:
354 messages
Followed by:
5 members
11
Wed Oct 04, 2006 8:24 pm
OA:

Sol: 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 = 13^4 *48*47 ---> choice A

### Best Conversation Starters

1 lheiannie07 116 topics
2 LUANDATO 67 topics
3 swerve 66 topics
4 ardz24 61 topics
5 AAPL 59 topics
See More Top Beat The GMAT Members...

### Most Active Experts

1 Scott@TargetTestPrep

Target Test Prep

213 posts
2 Brent@GMATPrepNow

GMAT Prep Now Teacher

177 posts
3 Jeff@TargetTestPrep

Target Test Prep

168 posts
4 Rich.C@EMPOWERgma...

EMPOWERgmat

133 posts
5 GMATGuruNY

The Princeton Review Teacher

126 posts
See More Top Beat The GMAT Experts