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GMATPrep2 - Combinations

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by zacharyz » Tue Jun 03, 2008 9:47 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 1 person in the crew has previous experience in space flight. How many different crews of thsi type are possible?

a) 432
b) 594
c) 864
d) 1330
e) 7980

OA is A
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by VP_Jim » Tue Jun 03, 2008 11:30 am
First, recognize that we have 12 choices for one spot on the team (the experienced person).

Now, we have to pick two inexperienced people. We have 9 choices for the first, and 8 choices for the second. Also, the order in which we pick them doesn't matter (e.g., a team of astronaut A and B is the same as a team of astronaut B and A). Thus, we have 36 different combinations of inexperienced astronauts [( 9*8 )/2!]

Finally, 12*36 = 432.

Hope this helps!
Jim S. | GMAT Instructor | Veritas Prep
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