From a group of 21 astronauts that includes 12 people with

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BTGmoderatorLU: Moderator; Posts: 2505; Joined: Sun Oct 15, 2017 1:50 pm; Followed by:6 members

From a group of 21 astronauts that includes 12 people with

by BTGmoderatorLU » Sat Oct 20, 2018 2:22 pm

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Source: GMAT Prep

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 A.

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Source: Beat The GMAT — Problem Solving | Sat Oct 20, 2018 2:22 pm

fskilnik@GMATH: GMAT Instructor; Posts: 1449; Joined: Sat Oct 09, 2010 2:16 pm; Thanked: 59 times; Followed by:33 members

From a group of 21 astronauts that includes 12 people with p

by fskilnik@GMATH » Sun Oct 21, 2018 12:17 pm

BTGmoderatorLU wrote:Source: GMAT Prep

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

$$21\,\,{\rm{astron}}\,\,\,\left\{ \matrix{
\,12\,\,{\rm{experts}} \hfill \cr
\,21 - 12 = 9\,\,{\rm{non}}\,{\rm{experts}} \hfill \cr} \right.$$
$$?\,\,\, = \,\,\,\,\# \,\,3\,{\text{people - group}}\,\,,\,\,{\text{exactly}}\,\,1\,\,{\text{expert}}$$
$$?\,\,\, = \,\,\,12 \cdot C\left( {9,2} \right)\,\,\, = 12 \cdot \frac{{9 \cdot 8}}{2} = \underleftrightarrow {9 \cdot 48\,\, = \,\,360 + 72}\,\,\, = \,\,\,432$$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.

Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8087; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Tue Oct 23, 2018 6:24 pm

BTGmoderatorLU wrote:Source: GMAT Prep

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.

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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