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A lottery winner from State F must match, in any order, 6 balls random

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A lottery winner from State F must match, in any order, 6 balls random [#permalink]

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New post 27 Aug 2017, 21:42
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Question Stats:

36% (02:44) correct 64% (01:52) wrong based on 39 sessions

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A lottery winner from State F must match, in any order, 6 balls randomly chosen from a single pool of balls numbered from 1 to 50. A lottery winner from State G must match, in any order, 5 balls randomly chosen from a first pool of balls numbered from 1 to 50 AND a “megaball,” randomly chosen from a second set of balls numbered from 1 to 50. The number of winning combinations in a single drawing of the lottery in State G is what percentage greater than the number of winning combinations in a single drawing of the lottery in State F?
A. 11%
B. 85%
C. 111%
D. 567%
E. 667%
[Reveal] Spoiler: OA

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Re: A lottery winner from State F must match, in any order, 6 balls random [#permalink]

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New post 27 Aug 2017, 22:04
For F: Total combination is \(50C_6\) = \(\frac{50*49*48*47*46*45}{6*5*4*3*2*1}\)

For G: Total combination is \(50C_5\)*\(5C_1\) = \(\frac{50*49*48*47*46}{5*4*3*2*1}\)*\(\frac{50}{1}\)

% greater = \(\frac{change}{smaller}\)*100

change = \(\frac{50*49*48*47*46}{5*4*3*2*1}\)*\(\frac{50}{1}\) - \(\frac{50*49*48*47*46*45}{6*5*4*3*2*1}\)

= \(\frac{50*49*48*47*46}{5*4*3*2*1}\) (50 - \(\frac{45}{6}\))

% greater = \(\frac{\frac{50*49*48*47*46}{5*4*3*2*1}(50 - \frac{45}{6})}{\frac{50*49*48*47*46*45}{6*5*4*3*2*1}}\)*100

= \(\frac{50 - \frac{45}{6}}{\frac{45}{6}}\)*100

= \(\frac{50*6 - 45}{45}\)*100

=566.66%

Thus Option D
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Re: A lottery winner from State F must match, in any order, 6 balls random [#permalink]

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New post 28 Aug 2017, 02:47
HolaMaven wrote:
For F: Total combination is \(50C_6\) = \(\frac{50*49*48*47*46*45}{6*5*4*3*2*1}\)

For G: Total combination is \(50C_5\)*\(5C_1\) = \(\frac{50*49*48*47*46}{5*4*3*2*1}\)*\(\frac{50}{1}\)

% greater = \(\frac{change}{smaller}\)*100

change = \(\frac{50*49*48*47*46}{5*4*3*2*1}\)*\(\frac{50}{1}\) - \(\frac{50*49*48*47*46*45}{6*5*4*3*2*1}\)

= \(\frac{50*49*48*47*46}{5*4*3*2*1}\) (50 - \(\frac{45}{6}\))

% greater = \(\frac{\frac{50*49*48*47*46}{5*4*3*2*1}(50 - \frac{45}{6})}{\frac{50*49*48*47*46*45}{6*5*4*3*2*1}}\)*100

= \(\frac{50 - \frac{45}{6}}{\frac{45}{6}}\)*100

= \(\frac{50*6 - 45}{45}\)*100

=566.66%

Thus Option D


HolaMaven , can you explain the one that I highlighted?

If 5C1 then it should be \(\frac{5}{1}\).
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A lottery winner from State F must match, in any order, 6 balls random [#permalink]

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New post 02 Sep 2017, 20:36
HolaMaven wrote:
A lottery winner from State F must match, in any order, 6 balls randomly chosen from a single pool of balls numbered from 1 to 50. A lottery winner from State G must match, in any order, 5 balls randomly chosen from a first pool of balls numbered from 1 to 50 AND a “megaball,” randomly chosen from a second set of balls numbered from 1 to 50. The number of winning combinations in a single drawing of the lottery in State G is what percentage greater than the number of winning combinations in a single drawing of the lottery in State F?
A. 11%
B. 85%
C. 111%
D. 567%
E. 667%



Hi...
Let's see the combinations of each..

Here you can do with probability too

State F
First ball picking probability is 1/50, next 1/49 and so on..
Since ORDER is not important, these 6 can be picked in 6! Ways..
So prob = \(\frac{1}{50}* \frac{1}{49}.....\frac{1}{45}*6!\)

State G
Similarly \(\frac{1}{50}* \frac{1}{49}.....\frac{1}{46}*5!*1/50\)
Final 1/50 is the megaball..

%={ \({\frac{1}{50}* \frac{1}{49}.....\frac{1}{45}*6!-\frac{1}{50}* \frac{1}{49}.....\frac{1}{46}*5!*1/50\)}/{\(\frac{1}{50}* \frac{1}{49}.....\frac{1}{46}*5!*1/50\)}*100

={\({\frac{6}{45}-\frac{1}{50}\)}/\(\frac{1}{50}\)*100
= \(\frac{5100}{9}=567%\)

D
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A lottery winner from State F must match, in any order, 6 balls random [#permalink]

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New post 06 Sep 2017, 08:18
Even though the concept is rather easy, the question is too calculation intensive to appear on the GMAT.

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A lottery winner from State F must match, in any order, 6 balls random   [#permalink] 06 Sep 2017, 08:18
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A lottery winner from State F must match, in any order, 6 balls random

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