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From a group of 21 astronauts that includes 12 people with

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From a group of 21 astronauts that includes 12 people with [#permalink] New post 01 Jun 2008, 04:52
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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 1 person in the crew has previous experience in space flight. How many different crews of this type are possible?
A) 432
B) 594
C) 864
D) 1330
E) 7980

OPEN DISCUSSION OF THIS QUESTION IS HERE: from-a-group-of-21-astronauts-that-includes-12-people-with-136299.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 05 Sep 2013, 00:14, edited 2 times in total.
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Re: Combinatorics problem [#permalink] New post 01 Jun 2008, 05:33
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japped187 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 1 person in the crew has previous experience in space flight. How many different crews of this type are possible?
A) 432
B) 594
C) 864
D) 1330
E) 7980


Hi
The answer is A for me
number of astronauts with previous experience = 12
Remaining =9
we need to pick exactly one from the first group
and 2 from the second group

(12C1)*(9C2)
=12*36= 432

what is the OA?

cheers
!!
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Re: Combinatorics problem [#permalink] New post 01 Jun 2008, 05:35
japped187 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 1 person in the crew has previous experience in space flight. How many different crews of this type are possible?
A) 432
B) 594
C) 864
D) 1330
E) 7980


12*9C2 = 432
are "different" combinations possible.
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Re: Combinatorics problem [#permalink] New post 04 Sep 2013, 21:45
zeenie wrote:
japped187 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 1 person in the crew has previous experience in space flight. How many different crews of this type are possible?
A) 432
B) 594
C) 864
D) 1330
E) 7980


Hi
The answer is A for me
number of astronauts with previous experience = 12
Remaining =9
we need to pick exactly one from the first group
and 2 from the second group

(12C1)*(9C2)
=12*36= 432

what is the OA?

cheers
!!

I have a problem with this question. actually i figure this out in this way (12C1)*(9C2)+(11C1)*(7C2)+(10C1)*(5C2)+(9C1)*(3C2).what i think is after draw 1 from the 12 and 2from the 9, so it is time to drew crews from the 11 and 7.
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Re: Combinatorics problem [#permalink] New post 04 Sep 2013, 22:06
Expert's post
august31707 wrote:
zeenie wrote:
japped187 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 1 person in the crew has previous experience in space flight. How many different crews of this type are possible?
A) 432
B) 594
C) 864
D) 1330
E) 7980


!!

I have a problem with this question. actually i figure this out in this way (12C1)*(9C2)+(11C1)*(7C2)+(10C1)*(5C2)+(9C1)*(3C2).what i think is after draw 1 from the 12 and 2from the 9, so it is time to drew crews from the 11 and 7.


No, In this case you have to perform two consecutive selections i.e. selection of a experienced astronaut from 12 experienced astronauts AND selection of two inexperienced astronauts from 9 inexperienced astronauts.

selection of a experienced astronaut from 12 experienced astronauts :- 12 C 1

AND ---------------------------------------------------------------------> Multiplication Sign

selection of two inexperienced astronauts from 9 inexperienced astronauts. 9 C 2

In the later event you will choose 2 astronauts from the pool of 9 astronauts simultaneously. Say from the five alphabets a, b, c, d, e you want select a pair of alphabet. Then you will select those alphabets in pairs such as ab, ac, ad, ae, bc, ....... this way.

So (12 C 1) AND (9 C 2) -------> (12 C 1) AND (9 C 2) -------> 432

Hope that Helps!
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Re: From a group of 21 astronauts that includes 12 people with [#permalink] New post 05 Sep 2013, 00:14
Expert's post
japped187 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 1 person in the crew has previous experience in space flight. How many different crews of this type are possible?
A) 432
B) 594
C) 864
D) 1330
E) 7980


C^1_{12}*C^2_9=12*36=432, where C^1_{12} is ways to select 1 astronaut with previous experience out of 12 and C^2_9 is ways to select 2 astronauts without experience out of 9 remaining astronauts (21-12=9).

Answer: A.

OPEN DISCUSSION OF THIS QUESTION IS HERE: from-a-group-of-21-astronauts-that-includes-12-people-with-136299.html
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Re: From a group of 21 astronauts that includes 12 people with   [#permalink] 05 Sep 2013, 00:14
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