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?
My solution: 14C5x14C6x14C3-5C1x6C1
Is this correct? Thanks in advance
depends on how many songs on an album.
You appear to have tried to calculate the result for an album of 5 songs.
But, your answer is too large. There are 14 songs in total.
If there are no duplicates, then once you have chosen the rock and country, there are 12 remaining songs, from which you want to pick 3.
So, there are 5*6*14C3 ways to pick them.
To find the number of different albums that can be formed using the given songs, we can use the principle of combinations.
First, let's consider the number of ways to choose the rock, country, and hip-hop songs separately.
For the rock songs, we have 5 options, and we need to choose at least 1. So the number of combinations is: 5C1 = 5.
Similarly, for the country songs, we have 6 options, and we need to choose at least 1. So the number of combinations is: 6C1 = 6.
Finally, for the hip-hop songs, we have 3 options, and we can choose 0 or more songs. So the number of combinations can be calculated as: 3C0 + 3C1 + 3C2 + 3C3 = 1 + 3 + 3 + 1 = 8.
Now, to find the total number of different albums, we need to multiply the combinations from each category together. So the total number of albums would be: 5 x 6 x 8 = 240.
Therefore, the correct answer to the question is 240, not 14C5 x 14C6 x 14C3 - 5C1 x 6C1.
If you still have any questions, feel free to ask!