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

_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372

2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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