Judges will select 5 finalists from the 7 contestants entered in a singing competition. The judges will then rank the

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M7MBA: Moderator; Posts: 2058; Joined: Sun Oct 29, 2017 4:24 amFollowed by: 5 members; Thanked: 1 times

by M7MBA » Thu Jul 30, 2020 11:21 am

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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?

A. 10
B. 21
C. 210
D. 420
E. 1,260

[spoiler]OA=C[/spoiler]

Source: Princeton Review

Source: Beat The GMAT — Problem Solving | Thu Jul 30, 2020 11:21 am

deloitte247: Legendary Member; Posts: 2214; Joined: Fri Mar 02, 2018 2:22 pmFollowed by: 5 members

Re: Judges will select 5 finalists from the 7 contestants entered in a singing competition. The judges will then rank th

by deloitte247 » Sat Aug 01, 2020 7:25 am

Total contestants = 7
Finalist needed = 5
Highest rank = 3
Judges will select 5 out of 7 contestants and how to select 3 top ratings from the 5.
$$7C_5\cdot5C_3$$
$$7C_5=\frac{7!}{5!\left(7-5\right)!}=\frac{7\cdot6\cdot5!}{5!\cdot2\cdot1}=\frac{42}{2}=21$$
and
$$5C_3=\frac{5!}{3!\left(5-3\right)!}=\frac{5\cdot4\cdot3!}{3!\cdot2\cdot1}=\frac{20}{2}=10$$
$$Therefore,\ 7C_5\cdot5C_3=21\cdot10=210$$
Answer = Option C

Ignite: Junior | Next Rank: 30 Posts; Posts: 13; Joined: Sat Aug 01, 2020 9:03 pm

Re: Judges will select 5 finalists from the 7 contestants entered in a singing competition. The judges will then rank th

by Ignite » Sat Aug 01, 2020 10:52 pm

This question is just asking us how many ways can the three candidates be 'Arranged' from the 7 initial.
We can ignore the initial 5 selection completely. The arrangement is important here,

Choosing 3 out of 7 = 7C3
Arranging the three = 3! ways

Thus, (7! / 3! 4!) * 3 ! = 210

Answer C

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8246; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

Re: Judges will select 5 finalists from the 7 contestants entered in a singing competition. The judges will then rank th

by Scott@TargetTestPrep » Sun Aug 02, 2020 8:55 am

M7MBA wrote: ↑
Thu Jul 30, 2020 11:21 am
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?

A. 10
B. 21
C. 210
D. 420
E. 1,260

[spoiler]OA=C[/spoiler]

Solution:

Since the finalists that do not make it to the top 3 ranks do not matter, we can ignore the selection of five finalists and calculate the number of ways to choose and order 3 contestants from a total of 7, which is 7P3 = 7!/(7 - 3)! = 7 x 6 x 5 = 210.

Answer: C

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