You cannot tell the marbles of the same color apart, so we have
21 positions

 o  o  o  o  o  o  o  o  o  o  o  o  o  o  o  o  o  o  o  o  o
 1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20 21

That's 21 choose 10 positions to place the 10 red marbles in. That's C(21,10)
That's leaves 11 choose 5 positions to place the white marbles in. That's
C(11,5). That leaves 6 choose 6 positions to place the blue marbles in.

Answer C(21,10)·C(11,5)·C(6,6) = 352716·462·1 = 162954792

Edwin