the Trip Aces game

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Fri May 07, 2010 5:32 am

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) 1/1440
(B) 1/720
(C) 1/120
(D) 1/56
(E) 1/44

The mind is everything. What you think you become. -Lord Buddha

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Source: Beat The GMAT — Problem Solving | Fri May 07, 2010 5:32 am

liferocks: Legendary Member; Posts: 576; Joined: Sat Mar 13, 2010 8:31 pmFollowed by: 1 member; Thanked: 97 times

by liferocks » Fri May 07, 2010 6:07 am

from a deck of 8 cards first card can be chosen in 8C1 or 8 ways

the deck will have 8-1 or 7 cards and the second can be chosen in 7C1 or 7 ways
the deck will have 7-1 or 6 cards and the second can be chosen in 6C1 or 6 ways

so 3 cards can be chosen in 8*7*6 ways

and the 3 aces can be chosen in 3*2*1 ways

so the probability is 3*2*1/8*7*6 or 1/56

Ans option D

"If you don't know where you are going, any road will get you there."
Lewis Carroll

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analyst218: Master | Next Rank: 500 Posts; Posts: 140; Joined: Fri Feb 05, 2010 2:43 pm; Thanked: 3 times; GMAT Score:720

by analyst218 » Fri May 07, 2010 11:12 am

sanju09 wrote: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) 1/1440
(B) 1/720
(C) 1/120
(D) 1/56
(E) 1/44

D.
3C3/8C3

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