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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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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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Abhishek Parikh
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Kudos [?]: 29 [1], given: 13

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

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

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

Kudos [?]: 12 [0], given: 796

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