From a group of 21 astronauts that includes 12 people

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VJesus12: Legendary Member; Posts: 2276; Joined: Sat Oct 14, 2017 6:10 amFollowed by: 3 members

by VJesus12 » Sat Feb 10, 2018 1:36 am

From a group of 21 astronauts that includes 12 people with previous experience in space flight, a 3-person crew is to be selected so that exactly one person in the crew has previous experience in space flight. How many different crews of this type are possible?

A. 432
B. 94
C. 864
D. 1330
E. 7980

The OA is the option A.

What are the formulas that I should use here? I am a little confused. How should I start solving this PS question? Thanks in advanced.

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Source: Beat The GMAT — Problem Solving | Sat Feb 10, 2018 1:36 am

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8157; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Sun Jul 28, 2019 9:24 am

VJesus12 wrote:From a group of 21 astronauts that includes 12 people with previous experience in space flight, a 3-person crew is to be selected so that exactly one person in the crew has previous experience in space flight. How many different crews of this type are possible?

A. 432
B. 94
C. 864
D. 1330
E. 7980

There are 12C1 = 12 ways to select a member with previous flight experience.

Since there are 21 - 12 = 9 members available to fill the remaining 2 slots in the crew, there are 9C2 = 9! / (2! x 7 !) = (9 x 8) / 2! = 36 ways to select 2 members with no previous flight experience.

So the total number of possible crews is 36 x 12 = 432.

Answer: A

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