There are 5 Rock songs, 6 country songs and 3 hip-hop songs. How many different albums can be formed using the songs if the albums should contain at least 1 Rock song and 1 Country song?
My solution: total number of songs is 5!6!3!=518,400 the number of different albums is 5x6x14C3 Is this correct. Thanks in advance.
As Steve already pointed out to you, the question is not clearly stated.
http://www.jiskha.com/display.cgi?id=1476444898
How many songs are on the album?
The way you stated it , we could have
3 R, 4 C, and 1 H as an album, or
1R, 1H, or ...
What about the order of the songs?
Once you choose a certain group of songs, they can then be arranged in different ways.
Is a different arrangements of the same songs a different album??
That is why it is so confusing. As I understand, there are 14 songs in total. The album should be formed from those songs and at least 1 rock song and 1 country song should be used.
To calculate the number of different albums that can be formed using the provided songs, we need to ensure that each album contains at least one Rock song and one Country song.
First, let's calculate the total number of albums without any restrictions. This can be done by multiplying the available options for each song category together:
Number of Rock songs = 5
Number of Country songs = 6
Number of Hip-hop songs = 3
Total number of albums without restrictions = Number of Rock songs * Number of Country songs * Number of Hip-hop songs = 5 * 6 * 3 = 90
Next, let's consider the restriction that each album should contain at least one Rock song and one Country song.
To calculate this, we can subtract the number of albums that don't include any Rock or any Country songs from the total number of albums without restrictions.
Number of albums without any Rock songs = Number of Country songs * Number of Hip-hop songs = 6 * 3 = 18
Number of albums without any Country songs = Number of Rock songs * Number of Hip-hop songs = 5 * 3 = 15
Number of albums without any Rock or Country songs = Number of Hip-hop songs = 3
Now, subtract the number of albums without any Rock or any Country songs from the total number of albums without restrictions:
Number of different albums = Total number of albums without restrictions - Number of albums without any Rock or Country songs
= 90 - 3
= 87
Therefore, the correct number of different albums that can be formed using the given songs, with at least one Rock song and one Country song each, is 87.