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# Select 5 numbers from the series of 1 to 20 (inclusive).

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Senior Manager
Joined: 25 Dec 2003
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Select 5 numbers from the series of 1 to 20 (inclusive). [#permalink]  12 Jul 2004, 07:25
Select 5 numbers from the series of 1 to 20 (inclusive). What is the probability that the selected number does not contain either 19 or 20.

Please explain procedure. (A simple one)
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Senior Manager
Joined: 05 Feb 2004
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Location: USA
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Is it: 1-19C3/21C5.......!
Director
Joined: 04 Jul 2004
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I think... it should be 18C5/20C5
Director
Joined: 05 May 2004
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Location: San Jose, CA
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Agree with JPV
1-20 20 numbers - 5 can be selected in 20C5 ways
exluding 19,20 there are 18 numbers - 5 can be selected in 18C5 ways
Prob= 18C5/20C5
CIO
Joined: 09 Mar 2003
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For me, it's easier to do: 18/20x17/19x16/18x15/17x14/16, which cancels out very nicely and gives you 21/38.

(all this assuming there can't be repeated numbers)
Intern
Joined: 29 Jun 2004
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what if the same question had a little twist.....find the probability either 19 0r 20.....can any1 explain
Senior Manager
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Hi
then it will be

Prob= 1-(18C5/20C5)

1-(21/38)

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Manager
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Re: Probs question [#permalink]  14 Jul 2004, 07:01
carsen wrote:
Select 5 numbers from the series of 1 to 20 (inclusive). What is the probability that the selected number does not contain either 19 or 20.

Please explain procedure. (A simple one)

# of combinations of 5 numbers which doesn't contain either 19 or 20 is C[5,18].

# of possible combinations = C[5,20].

P(result) = C[5,18]/C[5,20] = (18!/13!5!)/(20!/15!5!) = 15*14/(20*19) = 3/4*14/19 = 42/76 = 21/38.
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thanks! Need some advice i have my gmat on monday and i been working only from kaplan, OG and once in a while from this forum.....do u think OG is reflective of the real quant questions and how close is powerprep tests to the real tests...any advice will be helpful
Manager
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sid_477 wrote:
thanks! Need some advice i have my gmat on monday and i been working only from kaplan, OG and once in a while from this forum.....do u think OG is reflective of the real quant questions and how close is powerprep tests to the real tests...any advice will be helpful

OG is very reflective of the real GMAT test, if you run a regression of actual GMAT scores on PP scores and Kaplan scores, you'll see that PP scores are more meaningful in this regression.

But there is of course one detail: OG and PP often do not contain hard problems, which appear on the test (deviation, mean, median, etc.; probability, combination, etc.). With this exception, OG and PP provide pretty real questions.
CIO
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I agree with emmanuel,

The OG is definately the source for real GMAT questions - anything else is someone's interpretation of them. But the hardest CAT questions aren't in the OG at all. I think the last 200 of the multiple choice and the last 100 of the data sufficiency are better than the first sets of questions - that's because they were the ones added for the 10th edition, so they're newer.

I take the GMAT every 6 months, so I speak from much experience.
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