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 album should contain at least 1 rock song and 1 country song?
5*6*2^12
You don't say how many songs are to be used, so after choosing the 1 each of country and rock, there are 12 remaining songs. The power set of 12 elements has 2^12 members.
I don't think that is the correct answer. The total number of songs 5+6+3 so I guess 14C5x14C6x14C3-5C1x6C1 I'm just very confused. Thanks
To calculate the number of different albums that can be formed, we need to consider the combinations of rock, country, and hip-hop songs.
First, let's choose the rock song(s) for the album. Since we need at least 1 rock song, we have 5 choices for the first rock song. For the remaining songs, we can have anywhere from 0 to 4 more rock songs. We can represent this as:
Choose 1 rock song: C(5, 1)
Choose 0 to 4 additional rock songs: C(5, 0) + C(5, 1) + C(5, 2) + C(5, 3) + C(5, 4)
Next, let's choose the country song(s). Similarly, we have 6 choices for the first country song. For the remaining songs, we can have anywhere from 0 to 5 more country songs. This can be represented as:
Choose 1 country song: C(6, 1)
Choose 0 to 5 additional country songs: C(6, 0) + C(6, 1) + C(6, 2) + C(6, 3) + C(6, 4) + C(6, 5)
Now, to determine the total number of different albums, we need to multiply the number of choices for rock songs by the number of choices for country songs. In this case, we are choosing at least 1 rock song and 1 country song, so we multiply the above combinations together:
Total number of different albums = (C(5, 1) + C(5, 0) + C(5, 1) + C(5, 2) + C(5, 3) + C(5, 4)) * (C(6, 1) + C(6, 0) + C(6, 1) + C(6, 2) + C(6, 3) + C(6, 4) + C(6, 5))
By calculating these combinations, we find that there are a total of 12,120 different albums that can be formed using these songs.