Problem Solving

In a group of 8 semifinalist, all but 2 will advance to the final round. If in the final round only the top 3 will be awarded medals, then how many groups of medal winners are possible?
A. 20
B. 56
C. 120
D. 560
E. 720

narisipalli wrote:In a group of 8 semifinalist, all but 2 will advance to the final round. If in the final round only the top 3 will be awarded medals, then how many groups of medal winners are possible?
A. 20
B. 56
C. 120
D. 560
E. 720

not sure in my solution but anyway
all but 2 means that only 6 tems will play final (8-2=6)
we can select 3 teams to be awarded 6C3=20 ways, and these teams can divide 3 tops 3! ways
so 6C3*3!=120
my answer C

In a group of 8 semifinalist, all but 2 will advance to the final round. If in the final round only the top 3 will be awarded medals, then how many groups of medal winners are possible?
A. 20
B. 56
C. 120
D. 560
E. 720

D
8C2*6C3 = 560

narisipalli wrote:In a group of 8 semifinalist, all but 2 will advance to the final round. If in the final round only the top 3 will be awarded medals, then how many groups of medal winners are possible?
A. 20
B. 56
C. 120
D. 560
E. 720

8 teams, 3 awards
8C3=56 ways

the info "all but 2 advance to final stage" is useless... b'cos we are asked how many different groups of medal winners are possible. And all the 8 teams are equally likely to win the medals.
Suppose, only 3 teams advance. Would that change anything? Would the number of possibilities be 1? No.

Let me know OA.

It would always help if the author of the post mentions the source and OA.
Thanks.

iamseer wrote:

narisipalli wrote:In a group of 8 semifinalist, all but 2 will advance to the final round. If in the final round only the top 3 will be awarded medals, then how many groups of medal winners are possible?
A. 20
B. 56
C. 120
D. 560
E. 720

8 teams, 3 awards
8C3=56 ways

the info "all but 2 advance to final stage" is useless... b'cos we are asked how many different groups of medal winners are possible. And all the 8 teams are equally likely to win the medals.
Suppose, only 3 teams advance. Would that change anything? Would the number of possibilities be 1? No.

Let me know OA.

It would always help if the author of the post mentions the source and OA.
Thanks.

Me toooooo for 56 ways!!

iamseer wrote:
Let me know OA.

It would always help if the author of the post mentions the source and OA.
Thanks.

Thanks iamseer. 56 is the right answer.
Source: Princeton Review workbook