You have a deck of 60 cards: 15 Red, 45 Blue. You draw 6 cards. What are the odds that you draw 2 Red?

The number of possible hands of drawing any 6 cards from 60 = C(60,6) = 50063860

And from these possibilities we want to draw  2 red cards from 15 and 4 blue cards from 45

So, this gives us

C(15.2) * C(45, 4) = 15644475

So

15644475 / 50063860   = anout 31.25%

To get red-red-blue-blue-blue-blue would be 15/60 x 14/59 x 45/58 x 44/57 x 43/56 x 42/55.

But this is not the only arrangement; there are actually 15 ways to end with two reds and four blues, so take the above answer times 15.

This is Geno's answer.

As you can see it is the same as CPhill's answer.    :)

$$\left({\frac{{\mathtt{15}}}{{\mathtt{60}}}}\right){\mathtt{\,\times\,}}\left({\frac{{\mathtt{14}}}{{\mathtt{59}}}}\right){\mathtt{\,\times\,}}\left({\frac{{\mathtt{45}}}{{\mathtt{58}}}}\right){\mathtt{\,\times\,}}\left({\frac{{\mathtt{44}}}{{\mathtt{57}}}}\right){\mathtt{\,\times\,}}\left({\frac{{\mathtt{43}}}{{\mathtt{56}}}}\right){\mathtt{\,\times\,}}\left({\frac{{\mathtt{42}}}{{\mathtt{55}}}}\right){\mathtt{\,\times\,}}{\mathtt{15}} = {\mathtt{0.312\: \!490\: \!387\: \!277\: \!369\: \!3}}$$