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Ansh777
Total No of songs = 15 No repetition
No of New Songs= 9

Probability = (Number of a Favourable outcome) / (Total number of outcomes)

Total No of outcomes= Total no of ways of selecting first 2 songs = 15C2 = 15*14/2
No of favourable outcomes = No of ways of selecting first 2 songs both new = 9C2 =9*8/2

probability that the first 2 songs that the band performs will both be new = 9*8/15*14 = 12/35

Answer: C

When selecting favorable outcome,
why will it not be
15C9 * 9C2

where we first select the 9 new songs out of the 15 songs and then select the 2 songs from the 9? I am confused. Any help will be appreciated. Thank you!
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I understand what you are trying to do :
First select 9 songs out of 15 then 2 songs out of 9
But please note that :
- we have to select only 2 songs out of 9 new songs .
-There are only 9 new songs in 15
so even by your method also no of ways of selecting 9 new songs out of 15 (in which there are only 9 new songs) is 1
or
say 1, 2, 3,4, 5, 6, 7, 8, 9 stands for new songs and A, B, C, D, E, F stands for old
Then now try selecting 9 new songs out of this set of 15 songs { 1, 2, 3,4, 5, 6, 7, 8, 9, A, B, C, D, E, F}
There is only one method i.e. {1, 2, 3,4, 5, 6, 7, 8, 9}
Or by using combination: 9C9 = 1

-Therefore Favorable outcomes:
9C9*9C2 = 9C2

- By doing 15C9 you are actually mixing both new and old songs

its just unnecessary to do

Hope that helps !!

fireflyejd1

When selecting favorable outcome,
why will it not be
15C9 * 9C2

where we first select the 9 new songs out of the 15 songs and then select the 2 songs from the 9? I am confused. Any help will be appreciated. Thank you!
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Bunuel
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?

A. 1/7
B. 2/7
C. 12/35
D. 8/25
E. 23/35

The probability that the first two songs will be new is 9/15 x 8/14 = 3/5 x 4/7 = 12/35.

Answer: C
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