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A password on Mr. Wallace's briefcase consists of 5 digits..

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by rakeshd347 » Sun Sep 29, 2013 6:59 pm
A password on Mr. Wallace's briefcase consists of 5 digits. What is the probability that the password contains exactly three digit 6?

A. 860/90,000
B. 810/100,000
C. 858/100,000
D. 860/100,000
E. 1530/100,000

OA after some discussion.
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by theCodeToGMAT » Sun Sep 29, 2013 7:26 pm
(9 * 9 * 1 * 1 * 1)5!
___________________
10^5 * 3! * 2!

810
___
10^5

Answer [spoiler]{B}[/spoiler]
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by [email protected] » Mon Sep 30, 2013 11:04 pm
Hi rakeshd347,

For these types of questions, you have to be very careful about what "satisfies" the given question and what doesn't. For this prompt, we need three 6s and two "non-6s." However, ANY of the 3 values could be 6 while ANY of the 2 values could "not be 6." We can use the combination formula to assist us.

First, here's what we NEED: 6, 6, 6, non-6, non-6 (in every possible arrangement)

Mathematically, this is 1x1x1x9x9 = 81

Since any 3 numbers can be 6, we can use 5c3 to figure out all the possible ways to get exactly three 6s.

5c3 = 10 sets of three 6s.

81 x 10 = 810

With 5 digits, there are 100,000 total possibilities.

Final Answer: 810/100,000 = B

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Rich
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