In  12*11*10*9*8*7*6*5*4*3 = 239500800 ways.


It is the product of 10 consecutive integer numbers, starting from 12 in descending order.


1-st record to play can be any one of 12 records;

2-nd record to play can be any one of remaining 11 records;

3-rd record to play can be any one of remaining 10 records;

4-th record to play can be any one of remaining 9 records;


    . . . and so on . . . 


The last, 10-th record to play can be any one of remaining 3 records.


The product of these numbers, from 12 to 3, gives the answer.