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If five integers are selected from all the integers between 1 and 20

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Bunuel
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If five integers are selected from all the integers between 1 and 20 [#permalink] If five integers are selected from all the integers between 1 and 20  04 Dec 2022, 09:31
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If five integers are selected from all the integers between 1 and 20, inclusive, without replacement, what is the probability that the five integers will include both 10 and 20?

A. 17/38
B. 1/19
C. 1/20
D. 5/408
E. 1/380

 


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Re: If five integers are selected from all the integers between 1 and 20 [#permalink] If five integers are selected from all the integers between 1 and 20  04 Dec 2022, 09:42
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Bunuel wrote:
If five integers are selected from all the integers between 1 and 20, inclusive, without replacement, what is the probability that the five integers will include both 10 and 20?

A. 17/38
B. 1/19
C. 1/20
D. 5/408
E. 1/380



We need 5 integers, and 10 and 20 must be a part of those 5 integers. Hence besides 10 and 20, we need only 3 integers.

Number of ways of selecting 3 integers from 18 integers = 18C3

Note: We are taking 18 integers because 10 and 20 have been taken out.

Total ways of selecting 5 integers from 20 integers = 20C5

Required Probability = \(\frac{18C3 }{ 20C5}\) = \(\frac{1}{19}\)

Option B
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Re: If five integers are selected from all the integers between 1 and 20 [#permalink] If five integers are selected from all the integers between 1 and 20  26 Jan 2023, 21:34
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Solving using example and theory:

Say the question asks for 1 card only. The probability is 1/20.
Say the question asks to draw 10 cards. Then the probability to get that 1 card is 1/2.
So say the question asks to draw 5 cards. Then the probability to get that 1 card is 5/20, which is 1/4. BUTBUTBUT then, the question also asks you to have another card in the 5-deck; so it'll be (1/19 * 4) ... so together it'll be just 1/19
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Re: If five integers are selected from all the integers between 1 and 20 [#permalink] If five integers are selected from all the integers between 1 and 20  11 Feb 2024, 05:15
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Bunuel I got this question in gmat prep focus mock today , kindly change its tag..
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Re: If five integers are selected from all the integers between 1 and 20 [#permalink] If five integers are selected from all the integers between 1 and 20  11 Feb 2024, 11:18
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Archit3110 wrote:
Bunuel I got this question in gmat prep focus mock today , kindly change its tag..

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Can you please post a screenshot? Thank you!
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Re: If five integers are selected from all the integers between 1 and 20 [#permalink] If five integers are selected from all the integers between 1 and 20  12 Feb 2024, 10:29
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Bunuel wrote:
Archit3110 wrote:
Bunuel I got this question in gmat prep focus mock today , kindly change its tag..

­
Can you please post a screenshot? Thank you!

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Bunuel
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Re: If five integers are selected from all the integers between 1 and 20 [#permalink] If five integers are selected from all the integers between 1 and 20  12 Feb 2024, 10:32
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Archit3110 wrote:
Bunuel
Screen shot attached...
Bunuel wrote:
Archit3110 wrote:
Bunuel I got this question in gmat prep focus mock today , kindly change its tag..

­
Can you please post a screenshot? Thank you!

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Re: If five integers are selected from all the integers between 1 and 20 [#permalink] If five integers are selected from all the integers between 1 and 20  12 Feb 2024, 20:37
Asked: If five integers are selected from all the integers between 1 and 20, inclusive, without replacement, what is the probability that the five integers will include both 10 and 20?

Total cases = 20C5 = 15504
Favorable cases = 18C3 = 816 since 10 & 20 are already selected

The probability that the five integers will include both 10 and 20 = 816/15504 = 1/19

IMO B

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Re: If five integers are selected from all the integers between 1 and 20 [#permalink] If five integers are selected from all the integers between 1 and 20  16 Feb 2024, 04:57
Bunuel can you please solve only using probability and not combinations
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