Number of ways in which one or more than one CD can be selected? 
There are $12$ copies of Beatles CDs, $7$ copies of Pink Floyd CDs,
$3$ different CDs of Michael Jackson, and $2$ different CDs of
Madonna. Find the number of ways in which one or more than one CD can
be selected?

My solution approach :- 
No. of ways $1$ CD can be selected out of $12$ same CDs of Beatles = $1$
No. of ways $2$ CD can be selected out of $12$ same CDs of Beatles = $1$
No. of ways $3$ CD can be selected out of $12$ same CDs of Beatles = $1$
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No. of ways $12$ CD can be selected out of $12$ same CDs of Beatles = $1$
Hence total number of ways for selecting Beatles CDs = $1 \times 12 = 12$
Similarly for Pink Floyd CDs;
Total number of ways of selecting Pink Floyd CDs = $1 \times 7 = 7$
No. of ways $1$ CD can be selected out of $3$ different CDs of Michael Jackson = $3$
No. of ways $2$ CD can be selected out of $3$ different CDs of Michael Jackson = $3$
No. of ways $3$ CD can be selected out of $3$ different CDs of Michael Jackson = $1$
Hence total number of ways for selecting Michael Jackson CDs = $3+3+1 = 7$
No. of ways $1$ CD can be selected out of $2$ different CDs of Madonna = $2$
No. of ways $2$ CD can be selected out of $2$ different CDs of Madonna = $1$
Hence total number of ways for selecting Madonna CDs = $2+1 = 3$
Total number of ways in which one or more than one CD can be selected = $12 \times 7 \times 7 \times 3 = 1764$
But this is not the right answer that has been provided. What am I doing wrong? Can someone please help me on this?
Thanks in advance !!!
 A: Let me give you another approach , it will help you to calculate whatever you want.
I will make use of generating function , i guess you heard about it before. Then , lets start :
First of all , i want to write the generating function for $12$ identical Beatles CD's such that $$1 + x+ x^2 +x^3 +....+x^{12} =\frac{1-x^{13}}{1-x}$$
Secondly , write the generating function for $7$ identical Pink Floyd CD's such that
$$1+x+x^2+...+x^7 = \frac{1-x^8}{1-x}$$
Thirdly , write the generating function for $3$ different Michael Jackson CD's such that $$1 + 3x +3x^2 +x^3$$
Lastly ,write the generating function for $2$ different Madonna CD's such that
$$1+2x+x^2$$
Then , when we multiply them such that https://www.wolframalpha.com/input/?i=expanded+form+of+%28%281+-+x%5E13%29+%2F+%281-x%29%29+%28%281-x%5E8%29%2F%281-x%29%29+%281+%2B+3x+%2B+3x%5E2+%2Bx%5E3%29+%281+%2B2x+%2Bx%5E2%29
We can obtain the result which contain how many CD's can be selected in different numbers . However , we want all possibilities , so we must sum all coeffficients , it would give us $3328$ ,but we do not want the situation where none Cd's selected . It is clear that coefficient of $[x^0]$ is $1$ in the expansion , so we must subtract it from the total such that $$3328-1=3327$$
