• 1 Hour Free
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• Free Veritas GMAT Class
Experience Lesson 1 Live Free

Available with Beat the GMAT members only code

• 5 Day FREE Trial
Study Smarter, Not Harder

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

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

Available with Beat the GMAT members only code

• Magoosh
Study with Magoosh GMAT prep

Available with Beat the GMAT members only code

• Get 300+ Practice Questions

Available with Beat the GMAT members only code

• Free Trial & Practice Exam
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

## Difficult Math Problem #75 - Probability

This topic has 1 expert reply and 3 member replies
800guy Master | Next Rank: 500 Posts
Joined
27 Jun 2006
Posted:
354 messages
Followed by:
5 members
11

#### Difficult Math Problem #75 - Probability

Wed Dec 13, 2006 4:25 pm
The Full House Casino is running a new promotion. Each person visiting the casino has the opportunity to play the Trip Aces game. In Trip Aces, a player is randomly dealt three cards, without replacement, from a deck of 8 cards. If a player receives 3 aces, they will receive a free trip to one of 10 vacation destinations. If the deck of 8 cards contains 3 aces, what is the probability that a player will win a trip?

A. 1/336
B. 1/120
C. 1/56
D. 1/720
E. 1/1440

Need free GMAT or MBA advice from an expert? Register for Beat The GMAT now and post your question in these forums!
thankont Senior | Next Rank: 100 Posts
Joined
15 Dec 2006
Posted:
41 messages
Followed by:
1 members
Fri Dec 15, 2006 12:23 pm
One other approach is this one ( 3 /8 ).( 2/7 ).( 1/6 ) = 1/56 (since the question is without replacent).

800guy Master | Next Rank: 500 Posts
Joined
27 Jun 2006
Posted:
354 messages
Followed by:
5 members
11
Fri Dec 15, 2006 9:30 am
OA:

The probability of an event A occurring is the number of outcomes that result in A divided by the total number of possible outcomes.

There is only one result that results in a win: receiving three aces.

Since the order of arrangement does not matter, the number of possible ways to receive 3 cards is a combination problem.

The number of combinations of n objects taken r at a time is

C(n,r) = n!/(r!(n-r)!)

C(8,3) = 8!/(3!(8-3)!)
C(8,3) = 8!/(3!(5!))
C(8,3) = 40320/(6(120))
C(8,3) = 40320/720
C(8,3) = 56

The number of possible outcomes is 56.

Thus, the probability of being dealt 3 aces is 1/56.

thankont Senior | Next Rank: 100 Posts
Joined
15 Dec 2006
Posted:
41 messages
Followed by:
1 members
Fri Dec 15, 2006 12:23 pm
One other approach is this one ( 3 /8 ).( 2/7 ).( 1/6 ) = 1/56 (since the question is without replacent).

800guy Master | Next Rank: 500 Posts
Joined
27 Jun 2006
Posted:
354 messages
Followed by:
5 members
11
Fri Dec 15, 2006 9:30 am
OA:

The probability of an event A occurring is the number of outcomes that result in A divided by the total number of possible outcomes.

There is only one result that results in a win: receiving three aces.

Since the order of arrangement does not matter, the number of possible ways to receive 3 cards is a combination problem.

The number of combinations of n objects taken r at a time is

C(n,r) = n!/(r!(n-r)!)

C(8,3) = 8!/(3!(8-3)!)
C(8,3) = 8!/(3!(5!))
C(8,3) = 40320/(6(120))
C(8,3) = 40320/720
C(8,3) = 56

The number of possible outcomes is 56.

Thus, the probability of being dealt 3 aces is 1/56.

### Best Conversation Starters

1 lheiannie07 112 topics
2 swerve 64 topics
3 LUANDATO 64 topics
4 ardz24 61 topics
5 AAPL 57 topics
See More Top Beat The GMAT Members...

### Most Active Experts

1 Scott@TargetTestPrep

Target Test Prep

227 posts
2 Brent@GMATPrepNow

GMAT Prep Now Teacher

176 posts
3 Jeff@TargetTestPrep

Target Test Prep

168 posts
4 Rich.C@EMPOWERgma...

EMPOWERgmat

138 posts
5 GMATGuruNY

The Princeton Review Teacher

129 posts
See More Top Beat The GMAT Experts