Natural High School !!

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Ozlemg: Master | Next Rank: 500 Posts; Posts: 407; Joined: Tue Jan 25, 2011 9:19 amFollowed by: 7 members; Thanked: 25 times

by Ozlemg » Wed Jul 27, 2011 7:03 am

The students at Natural High School sell coupon books to raise money after-school programs. At the end of the coupon sale, the school selects six students to win prizes as follows: From the homeroom with the highest total coupon-book sales, the students with the first-, second- and third-highest sales receive $50, $30, $20, respectively; from the homeroom with the second-highest total coupon-book sales, the three highest-selling students receive $10 each. If Natural High School has ten different homerooms with eight student each, in how many different ways could the six prizes be awarded?

Do not calculate the actual number...Just the logic i wonder about...
Thnx

The more you suffer before the test, the less you will do so in the test!

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Source: Beat The GMAT — Problem Solving | Wed Jul 27, 2011 7:03 am

vineeshp: Legendary Member; Posts: 965; Joined: Thu Jan 28, 2010 12:52 amFollowed by: 34 members; Thanked: 156 times; GMAT Score:720

by vineeshp » Wed Jul 27, 2011 7:30 am

Challenging question, but it would be great if you post the full OA so we can work out a solution and verify our answer.

My understanding and Solution:
We can choose any one of the ten schools in 10 ways (10C1) and once a school is selected, there are 8 students to win the 1st three prices. So that can be done in 8P3 ways.
Hence 10 * 8P3 (=3360)

Next 2nd school can be selected from remaining 9 schools in 9 ways and each school has 3 identical winners (all get 10) which can be chosen in 8C3 ways. (504)

Now total number of ways of selecting the 6 winners is the product of the above 2.

Vineesh,
Just telling you what I know and think. I am not the expert.

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Ozlemg: Master | Next Rank: 500 Posts; Posts: 407; Joined: Tue Jan 25, 2011 9:19 amFollowed by: 7 members; Thanked: 25 times

by Ozlemg » Wed Jul 27, 2011 7:42 am

vineeshp wrote:Challenging question, but it would be great if you post the full OA so we can work out a solution and verify our answer.

My understanding and Solution:
We can choose any one of the ten schools in 10 ways (10C1) and once a school is selected, there are 8 students to win the 1st three prices. So that can be done in 8P3 ways.
Hence 10 * 8P3 (=3360)

Next 2nd school can be selected from remaining 9 schools in 9 ways and each school has 3 identical winners (all get 10) which can be chosen in 8C3 ways. (504)

Now total number of ways of selecting the 6 winners is the product of the above 2.

I do not have the exact number either. But Here is the steps.may they help to contsruct the formulas:

Break down the problem into 3 decisions you have to make:
1) Select 2 homerooms,1 with Highest sales and 1 with 2nd highest sales.(order matters here)
2)Select 3 Students from the highest sales Homeroom, again here order matters as depending on the position the value of the prize differs
3)select 3 students from the 2nd highest sales homeroom, here the order doesn't matter as all 3 will receive the same prize.

The more you suffer before the test, the less you will do so in the test!

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