There are usually two methods of solution for his type of problem, a method based on counting, as used by Melody and CPhill, and a basic probability method.

The counting method has already been discussed, so here is the probability method.

Suppose that the six smarties fall in the sequence BBBBOO, where B represents a blue smartie and O one of the other colours.

The probability of that sequence happening will be

(6/19)*(5/18)*(4/17)*(3/16)*(13/15)*(12/14).

If you consider any other sequence consisting of four blues and two others, the individual fractions will be different but the combined top and bottom lines will be the same.

So, for example, if the sequence happened to be OBBOBB, the probability would be (13/19)*(6/18)*(5/17)*(12/16)*(4/15)*(3/14).

Different fractions, but the combined top line is still 13*12*6*5*4*3 and the bottom line 19*18*17*16*15*14.

So, the overall probability will be this probability multiplied by the number of possible sequences consisting of four blues and two others, that is,

(6/19)*(5/18)*(4/17)*(3/16)*(13/15)*(12/14)*6C4 = 0.0028748*15 = 0.0431(4dp).