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sana.noor: Legendary Member; Posts: 512; Joined: Mon Jun 18, 2012 11:31 pmFollowed by: 20 members; Thanked: 42 times

by sana.noor » Tue Sep 24, 2013 10:03 pm

In a business school case competition, the top three teams receive cash prizes of $5,000, $3,000, and $2,000, respectively, while the remaining teams are not ranked and do not receive any prizes. There are 6 participating teams, named Team A, Team B, Team C, Team D, Team E, and Team F. If Team A wins one of the prizes, Team B will also win one of the prizes. How many outcomes of the competition are possible?
a)18
b)20
c)54
d)84
e)120

OA is D

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Source: Beat The GMAT — Problem Solving | Tue Sep 24, 2013 10:03 pm

theCodeToGMAT: Legendary Member; Posts: 1555; Joined: Tue Aug 14, 2012 11:18 pmFollowed by: 34 members; Thanked: 448 times; GMAT Score:650

by theCodeToGMAT » Tue Sep 24, 2013 10:51 pm

A B C D E F

Two scenarios are possible:

CASE 1: A wins - consider A & B part of same group(2C2) and other as part of other group (4C1)

then --> 3!(2C2 x 4C1) = 24 Ways

Case 2: A doesnt Win -- Other group comprises of 5 teams out of which we need to select 3

then --> 3!(5C3) = 60 ways

Answer = 60 + 24 = 84 ways [spoiler]{D} [/spoiler]

R A H U L

ganeshrkamath: Master | Next Rank: 500 Posts; Posts: 283; Joined: Sun Jun 23, 2013 11:56 pmFollowed by: 26 members; Location: Bangalore, India; Thanked: 97 times; GMAT Score:750

by ganeshrkamath » Tue Sep 24, 2013 11:22 pm

sana.noor wrote:In a business school case competition, the top three teams receive cash prizes of $5,000, $3,000, and $2,000, respectively, while the remaining teams are not ranked and do not receive any prizes. There are 6 participating teams, named Team A, Team B, Team C, Team D, Team E, and Team F. If Team A wins one of the prizes, Team B will also win one of the prizes. How many outcomes of the competition are possible?
a)18
b)20
c)54
d)84
e)120

OA is D

If A is one of the winners : A,B,x
Total possibitities = 4C1 = 4

If A is not one of the winners : x,y,z
Total possibilities = 5C3 = 5C2 = 5*4/2 = 10

Now any of these can take any prize
So total combinations = 3! = 6

Grand total = (4 + 10) * 6 = 14*6 = 84

Choose d

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[email protected]: Elite Legendary Member; Posts: 10391; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Wed Sep 25, 2013 12:17 am

Hi sana.noor,

Each of the other explanations is mathematically correct. Here's another way to organize the "options"

Teams: A, B, C, D, E, F

With A:

A, B, _

ABC = (3)(2)(1) = 6 options
ABD = 6 options
ABE = 6 options
ABF = 6 options

Total options with A = 24

Without A:

B, C, D, E, F

_ _ _

(5)(4)(3) = 60 options without A

24 + 60 = 84 options

Final Answer: D

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