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Jane has stored three albums on her iPod. The first album consists of 11 songs by Frank Sinatra, the second album consists of 13 songs by Cliff Richard, including "Congratulations and Celebrations", and the third album consists of 8 songs by John Denver. She programs the shuffle function on her iPod to randomly select 10 songs from the three albums, not repeating any of the songs.Find the probability that in one run of the shuffle she will definitely listen to “Congratulations and Celebrations”.

Question

Jane has stored three albums on her iPod. The first album consists of 11 songs by Frank Sinatra, the second album consists of 13 songs by Cliff Richard, including "Congratulations and Celebrations", and the third album consists of 8 songs by John Denver. She programs the shuffle function on her iPod to randomly select 10 songs from the three albums, not repeating any of the songs.

Find the probability that in one run of the shuffle she will definitely listen to “Congratulations and Celebrations”.

check_circleAnswer
Step 1

In this question, there is total 32 songs collection out of which 11 songs by Frank Sinatra, 13 songs by Cliff Richard and 8 songs by John Denver including one song “Congratulations and Celebrations”

Step 2

If we have selected a question ""Congratulations and Celebrations" then now we have to select the 9 out...

32
Total no. of ways to select the 10 songs out of 32
10
32!
10x22!
64512240
No. of ways to select 10 songs out of
31
=1x
09
which 1 is "Congratulations and Celebrations
31!
= 1x
9!x 22!
= 20160075
No. of ways to select 10 songs out which
C
"Congratulations and Celebrations",
Total no. of ways to select 10 songs
Now, Probability that in one shuffle run she
one 1s
. will definitely listen "Congratulations and Celebrations")
20160075
64512240
5
-0.3125
16
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32 Total no. of ways to select the 10 songs out of 32 10 32! 10x22! 64512240 No. of ways to select 10 songs out of 31 =1x 09 which 1 is "Congratulations and Celebrations 31! = 1x 9!x 22! = 20160075 No. of ways to select 10 songs out which C "Congratulations and Celebrations", Total no. of ways to select 10 songs Now, Probability that in one shuffle run she one 1s . will definitely listen "Congratulations and Celebrations") 20160075 64512240 5 -0.3125 16

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