IMHO answer is A (i.e. 15624).
Reasoning:
<pre-requisite>
How many ways are there to choose any number of things out of n things?
So, we can select 0 out of n things, 1 out of n things and so on...
hence the formula will be:
nC0 + nC1 + nC2 + ..... + nCn = 2^n
From this we can deduce:
How many ways are there to choose atleast one out of n things?
A:
(2^n) - 1 (as nC0 = 1)
</pre-requisite>
As you have 5 rock songs, how many songs can you pick to use in your album? You have to select at least one hence:
No of ways to choose Rock songs = (2^5) - 1 = 31
Similiarly, number of ways to choose Carnatic songs for your album = 2^6 - 1 = 63.
But it does not say that we HAVE to choose a indi-pop song... hence, number of ways to choose indi-pop song = 2^3 = 8.
Remember the way to count, if there are 3 things to do one after another, with combinations of say M, N & P, then total ways of doing it is M*N*P.
Thus our total count should be a multiple of the three values we calculated earlier.
= 31 * 63 * 8 = 15624.
Cheers,
Dubes
