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There are 5 Rock songs, 6 Pop songs, and 3 Jazz. How many different

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Re: There are 5 Rock songs, 6 Pop songs, and 3 Jazz. How many different  [#permalink]

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New post 20 Apr 2016, 03:02
Hi, Bunuel

Sorry, I can not understand the concept at all. please as usual, give the concept first and then give the solution steps.
I always learn from your introduction which may include basics or advanced concepts to save time in test.
Many thanks for your help.
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Re: There are 5 Rock songs, 6 Pop songs, and 3 Jazz. How many different  [#permalink]

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New post 20 Apr 2016, 03:14
hatemnag wrote:
Hi, Bunuel

Sorry, I can not understand the concept at all. please as usual, give the concept first and then give the solution steps.
I always learn from your introduction which may include basics or advanced concepts to save time in test.
Many thanks for your help.


Let's consider in how many ways we can build an album with 5 Rock songs if the albums should contain at least one Rock song. Each of the 5 songs can either be included in the album or not. For example, song #1 can be in the album or can be excluded from the album. Thus each of the 5 songs has 2 options in the album/not in the album. 2*2*2*2*2 = 2^5 = 32 options in total. But those 32 combinations include one combination for which we counted all songs as not included, thus for the album to have at least 1 rock song we should subtract that combination, which gives us 32-1=31 albums with at least 1 rock song.

Hope it helps.
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Re: There are 5 Rock songs, 6 Pop songs, and 3 Jazz. How many different  [#permalink]

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New post 20 Apr 2016, 05:30
Ok. I got it. I see that this concept is not traditional so when I should know that the solution does not need the traditional formula of Combination or Permutation or such knowledge will be acquired by practice ?
Many thanks Bunuel for caring.
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Re: There are 5 Rock songs, 6 Pop songs, and 3 Jazz. How many different  [#permalink]

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New post 22 Apr 2016, 00:00
Bunuel wrote:
hatemnag wrote:
Hi, Bunuel

Sorry, I can not understand the concept at all. please as usual, give the concept first and then give the solution steps.
I always learn from your introduction which may include basics or advanced concepts to save time in test.
Many thanks for your help.


Let's consider in how many ways we can build an album with 5 Rock songs if the albums should contain at least one Rock song. Each of the 5 songs can either be included in the album or not. For example, song #1 can be in the album or can be excluded from the album. Thus each of the 5 songs has 2 options in the album/not in the album. 2*2*2*2*2 = 2^5 = 32 options in total. But those 32 combinations include one combination for which we counted all songs as not included, thus for the album to have at least 1 rock song we should subtract that combination, which gives us 32-1=31 albums with at least 1 rock song.

Hope it helps.


hi Bunnuel

if the question stated that albums should contain at least 2 Rock songs, then do i undestand correctly that we would subtract 6 (2^5-6=26)?
TIA
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There are 5 Rock songs, 6 Pop songs, and 3 Jazz. How many different  [#permalink]

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New post 10 May 2016, 16:20
Can someone pls explain why we are not doing 2^4 and 2^5 (instead of 2^5 - 1 and 2^6 - 1) while considering rock and pop songs?

Bunuel can you pls address this question.
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Re: There are 5 Rock songs, 6 Pop songs, and 3 Jazz. How many different  [#permalink]

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New post 10 May 2016, 23:00
nmitra wrote:
Can someone pls explain why we are not doing 2^4 and 2^5 (instead of 2^5 - 1 and 2^6 - 1) while considering rock and pop songs?

Bunuel can you pls address this question.


This was explained several times:
there-are-5-rock-songs-6-pop-songs-and-3-jazz-how-many-different-57548.html#p1502655
there-are-5-rock-songs-6-pop-songs-and-3-jazz-how-many-different-57548.html#p1524116
there-are-5-rock-songs-6-pop-songs-and-3-jazz-how-many-different-57548-20.html#p1674836
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
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Re: There are 5 Rock songs, 6 Pop songs, and 3 Jazz. How many different  [#permalink]

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New post 11 May 2016, 01:43
Very Simple, each song can be either included or not included
So total ways 2^3∗(2^5)(2^6)

but this includes the no when no rock and no pop song is there
so required ans 2^3∗(2^5−1)(2^6−1)=15,624
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Re: There are 5 Rock songs, 6 Pop songs, and 3 Jazz. How many different  [#permalink]

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New post 10 Jun 2016, 21:02
boksana wrote:
There are 5 Rock songs, 6 Pop songs, and 3 Jazz. How many different albums can be formed using the above repertoire if the albums should contain at least one Rock song and one Pop song?

A. 15,624
B. 16,384
C. 6,144
D. 384
E. 240


I have solved this with a bit different approach. Can someone help me where I went wrong in this approach..
We need atleast one Rock song => 5c1 ways to select one rock song
We need atleast one Pop song => 6c1 ways to select one pop song
In the remaining 12 songs, we can take any number of songs ranging from 0 to 12 => 2^12

All put together , we have 5c1 * 6c1 * 2^12

But none of the options match this. Where did I go wrong..
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Re: There are 5 Rock songs, 6 Pop songs, and 3 Jazz. How many different  [#permalink]

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