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?

therefore the number of ways of choosing rock songs = ${2}^{5}=32$

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 = ${2}^{6}-1$ [at least one carnatic should be chosen]

i.e. 64-1 = 63 ways

the number of ways of choosing hindi pop songs = ${2}^{3}=8$

thus the number of different album that can be formed

= 31*63*8

= 15624

hope this helps you

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