There are 5 rock songs, 6 Carnatic songs and 3 Hindi pop songs. How many different albums can be formed using the above repertoire, if each album should contain at least 1 rock and 1 Carnatic?

there are 2n ways of choosing n objects.
therefore the number of ways of choosing rock songs = 25=32
since album should contain at least 1 rock song , the number of ways of choosing rock songs = 32-1 =31
the number of ways of choosing carnatic song = 26-1 [at least one carnatic should be chosen]
i.e. 64-1 = 63 ways
the number of ways of choosing hindi pop songs = 23=8
thus the number of different album that can be formed 
= 31*63*8
= 15624 

hope this helps you

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