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A certain band will perform 15 different songs in random ord

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Carcass
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A certain band will perform 15 different songs in random ord [#permalink] New post   28 Dec 2019, 13:16
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A certain band will perform 15 different songs in random order, and no song will be performed twice. If 9 of the songs are new, what is the probability that the first 2 songs that the band performs will both be new?


Give your answer as a fraction.


Show: :: OA
\(\frac{12}{35}\)
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uchihaitachi
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Re: A certain band will perform 15 different songs in random ord [#permalink] New post   29 Dec 2019, 01:00
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We have to select two songs such that both of them are new.
Total new songs available = 9
Probability = \(\frac{9C2}{15C2}\) = \(\frac{9*8}{15*14}\)

Probability = \(\frac{12}{35}\)
Carcass wrote:
A certain band will perform 15 different songs in random order, and no song will be performed twice. If 9 of the songs are new, what is the probability that the first 2 songs that the band performs will both be new?


Give your answer as a fraction.


Show: :: OA
\(\frac{12}{35}\)
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RSQUANT
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Re: A certain band will perform 15 different songs in random ord [#permalink] New post   09 Jan 2020, 01:22
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Carcass wrote:
A certain band will perform 15 different songs in random order, and no song will be performed twice. If 9 of the songs are new, what is the probability that the first 2 songs that the band performs will both be new?


Give your answer as a fraction.


Show: :: OA
\(\frac{12}{35}\)


First and foremost the question is about arrangement and not selection

The Random experiment is about arranging 15 distinct songs which is 15!

The event is about arranging 2 new songs at the start (9P2) and then the remaining 13 songs (13!)

[9P2 * 13!][/15!]

= 12/35
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nerd77
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Re: A certain band will perform 15 different songs in random ord [#permalink] New post   20 Apr 2020, 16:36
I know everyone is doing it the 9c2/15c2 way..but it doesn't make sense to me this way since order wouldn't matter for the first two as long as they were new. So those would actually be combinations, no? (9*8)/2! * (15*14)/2! which doesn't yield correct answer.

I think its just a reg probability question favorable/total= 9/15 * 8/14 = 12/35

But I'm not sure.
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gmatclubot
Re: A certain band will perform 15 different songs in random ord [#permalink]
20 Apr 2020, 16:36
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