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Judges will select 5 finalists from the 7 contestants [#permalink]
17 Jan 2005, 13:39

Judges will select 5 finalists from the 7 contestants entered in a singing competition. The judges will then rank the contestants and award prizes to the 3 highest ranked contestants: a blue ribbon for first place, a red ribbon for second place, and a yellow ribbon for third place. How many different arrangements of prize-winners are possible?

I also figured another approach to this. The whole logic of selecting 5 out of 7 is just to throw us in a loop. In the end, there will be three candidates from the 7 to get the prizes.

However since order matters, its a permuation issue.
i.e: 7 possible choices for 1st place, 6 for second and 5 for third.

I also figured another approach to this. The whole logic of selecting 5 out of 7 is just to throw us in a loop. In the end, there will be three candidates from the 7 to get the prizes.

However since order matters, its a permuation issue. i.e: 7 possible choices for 1st place, 6 for second and 5 for third.

So total possible arrangement = 7*6*5=210

thats an easier and much clearer route to take.. Gayathri...thanks..

Well i can explain why the answer is 210.
The principle of choice is being tested here and i think here it goes:

First out of 5 finalist out of 7 contestants are selected, meaning order does not matter it's just 5 people from 7 people thus we use 7C5 and we get 21

Then out of these 5, 3 contestants are ranked such that: a blue ribbon for first place, a red ribbon for second place, and a yellow ribbon for third place (this means order matters because it asks for different "arrangement" of prize winners) thus we use 5P3 and we get 10.

Well i can explain why the answer is 210. The principle of choice is being tested here and i think here it goes:

First out of 5 finalist out of 7 contestants are selected, meaning order does not matter it's just 5 people from 7 people thus we use 7C5 and we get 21

Then out of these 5, 3 contestants are ranked such that: a blue ribbon for first place, a red ribbon for second place, and a yellow ribbon for third place (this means order matters because it asks for different "arrangement" of prize winners) thus we use 5P3 and we get 10.

21 * 10 = 210

Folaa3, what do u think if within 3 contestants A,B,C, the order can change, first A, second B, third C or first B, second C, third A. So # of ways to arrange 3 best winners are 3!