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tttrn333: Junior | Next Rank: 30 Posts; Posts: 25; Joined: Thu Sep 08, 2011 8:06 am; Followed by:1 members

Prize Combo

by tttrn333 » Mon Sep 19, 2011 6:58 pm

In a business school case competition, the top three teams receive cash prizes of $5,000,$3000,$2000.
If there are 6 participating team, A,B,C,D,E,F. If A wins one prize and B wins another, how many outcomes are possible?

How I am solving:

Since A,B need to be in and since order matters, I assume its a set of 3. A,B, and O (other). Ways to arrange them is 3!=6

Since there are 4 different ways O can be (C,D,E,F). Answ= 6*4=24.

This is however wrong. Can someone explain?

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Source: Beat The GMAT — Problem Solving | Mon Sep 19, 2011 6:58 pm

amit2k9: Master | Next Rank: 500 Posts; Posts: 461; Joined: Tue May 10, 2011 9:09 am; Location: pune; Thanked: 36 times; Followed by:3 members

by amit2k9 » Mon Sep 19, 2011 7:49 pm

A,B can win prizes in 3c2 * 2! ways = 6
3c2 - 3 positions among which any 2 can be filled. 2! - between AB the combinations possible.

last position can be taken by 4c1 ways
thus, when AB are present = 6* 4 = 24 ways

when A is not present, remaining positions can be filled by any of the 5 teams
hence 5*4*3 = 60 ways

thus total = 60+24 = 84 ways.

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pm; Location: Milpitas, CA; Thanked: 1854 times; Followed by:523 members; GMAT Score:770

by Anurag@Gurome » Mon Sep 19, 2011 8:02 pm

tttrn333 wrote:In a business school case competition, the top three teams receive cash prizes of $5,000,$3000,$2000.
If there are 6 participating team, A,B,C,D,E,F. If A wins one prize and B wins another, how many outcomes are possible?

How I am solving:

Since A,B need to be in and since order matters, I assume its a set of 3. A,B, and O (other). Ways to arrange them is 3!=6

Since there are 4 different ways O can be (C,D,E,F). Answ= 6*4=24.

This is however wrong. Can someone explain?

The last part of the problem should read as "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?"

Solution:
This means that Case 1) If A is selected, then B is also selected. So, the total number of all possible arrangements is 4C1 * 3! = 24

Case 2) If A is not there, anybody can be selected. Note that the question does not mean that 'If A is not there, B will not be there.' Here the number of arrangements possible is 5P3 = 60.

So, total number of outcomes possible is 24+60 = 84.

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Gurome, Inc.
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