here are 5 Rock songs, 6 karnatic songs and 3 Indi pop songs. How many different albums can be formed using the above albums should contain at least 1 Rock song and 1 karnatic song?  Choose the correct option
A) 36254
B) 45124
C) 15624
D) 45654
E) 36254
There are 2n ways of choosing ‘n’ objects. For e.g. if n = 3, then the three objects can be chosen in the following 23 ways - 3C0 ways of choosing none of the three, 3C1 ways of choosing one out of the three, 3C2 ways of choosing two out of the three and 3C3 ways of choosing all three.   In the given problem, there are 5 Rock songs. We can choose them in 25 ways. However, as the problem states that the case where you do not choose a Rock song does not exist (at least one rock song has to be selected), it can be done in 25 - 1 = 32 - 1= 
<gadget id="calculator">32 - 1</gadget>
<output>31</output>
31 ways.   Similarly, the 6 Carnatic songs, choosing at least one, can be selected in 26 - 1= 64 - 1= 
<gadget id="calculator">64 - 1</gadget>
<output>63</output>
63 ways.   And the 3 Indi pop can be selected in 23= 8 ways. Here the option of not selecting even one Indi Pop is allowed.   Therefore, the total number of combinations = 31 * 63 * 8= 
<gadget id="calculator">31 * 63 * 8</gadget>
<output>15_624</output>
15624   Ans: 15624
<result>C</result>
here are 5 Rock songs, 6 karnatic songs and 3 Indi pop songs. How many different albums can be formed using the above albums should contain at least 1 Rock song and 1 karnatic song?