Probability query

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Probability query

by prernamalhotra » Tue May 13, 2014 12:08 am
Hi,

Can you please help with the below mentioned problem:

A certain university will select 1 of 7 candidates eligible to fill a position in mathematics department and 2 of 10 candidates eligible to fill 2 identical positions in computer science department. If none of the candidates is eligible for a position in both departments, how many different sets of 3 candidates are there to fill the 3 positions?

A) 42
B) 70
C) 140
D) 160
E) 315


Thank you,
Prerna

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by Brent@GMATPrepNow » Tue May 13, 2014 12:51 am
prernamalhotra wrote: A certain university will select 1 of 7 candidates eligible to fill a position in mathematics department and 2 of 10 candidates eligible to fill 2 identical positions in computer science department. If none of the candidates is eligible for a position in both departments, how many different sets of 3 candidates are there to fill the 3 positions?

A) 42
B) 70
C) 140
D) 160
E) 315
We can take the task of filling both positions and break it into stages.

Stage 1: Fill the 1 math position
There are 7 candidates, so we can complete stage 1 in 7 ways

Stage 2: Fill the 2 computer science positions
Note that the order in which we select candidates doesn't matter. For example, selecting candidate B and then candidate C is the same as selecting candidate C and then candidate B. So, we can use combinations here.
We can select 2 candidates from 10 in 10C2 ways (= 45 ways)

Aside: If anyone is interested, we have a free video on calculating combinations (like 10C2) in your head: https://www.gmatprepnow.com/module/gmat-counting?id=789

By the Fundamental Counting Principle (FCP), we can complete the two stages (and thus fill the three positions in (7)(45) ways ([spoiler]= 315 ways[/spoiler])

Answer: E
--------------------------

Note: the FCP can be used to solve the majority of counting questions on the GMAT. For more information about the FCP, watch our free video: https://www.gmatprepnow.com/module/gmat-counting?id=775

Then you can try solving the following questions:

EASY
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MEDIUM
- https://www.beatthegmat.com/combinatoric ... 73194.html
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DIFFICULT
- https://www.beatthegmat.com/wonderful-p- ... 71001.html
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Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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