permutation/combination

vaibhav101 wrote:there are 5 rock songs, 6 carnatic songs and 3 indi pop songs . How many different albums can be formed using the above repertoire if the album should contain at least 1 rock song and 1 carnatic song?

A 15624
B 16384
C 6144
D 240
E 8123

This question is a little too ambiguous to be an official GMAT question.
Let's say X, Y and Z represents 3 different songs.
Is an album with song X first, song Y second and song Z third considered DIFFERENT FROM an album with song Z first, song X second and song Y third?
The answer to this question is not apparent in the wording.

Cheers,
Brent

vaibhav101 wrote:there are 5 rock songs, 6 carnatic songs and 3 indi pop songs . How many different albums can be formed using the above repertoire if the album should contain at least 1 rock song and 1 carnatic song?

A 15624
B 16384
C 6144
D 240
E 8123

Each song can either be included in the album or excluded from the album, so each song has two choices. Since there are 14 songs, the number ways to form an album is 2^14 = 16,384 if there are no restrictions. (Notice that 2^14 is also equal to 2^5 x 2^6 x 2^3 where the exponents 5, 6 and 3 are the number of rock, carnatic, and indi pop songs, respectively.)

However, the album must contain at least 1 rock song and 1 carnatic song. Of the 2^5 = 32 ways to include any number (from 0 to 5) of rock songs, there is only 1 way that no rock song is included, so the number of ways to include at least 1 rock song is 32 - 1 = 31. Similarly, Of the 2^5 = 64 ways to include any number (from 0 to 6) of carnatic songs, there is only 1 way that no carnatic song is included, so the number of ways to include at least 1 carnatic song is 64 - 1 = 63. Note that there are no restrictions on the number of indi pop songs, so we have 2^3 = 8 ways to choose the indi pop songs. Therefore, the number of ways to include at least 1 rock song and 1 carnatic song in the album is:

31 x 63 x 8 = 15,624

Answer: A