(no subject)

[futurebird]

An urn contains 5 white 7 blue and 9 yellow marbles. What is the probability you will have the same number of white and yellow marbles if you draw 6 marbles without replacement?

I solved this in cases:
These are the ways you can have the same number of yellow and white marbles:

Case 1.
6 - B

Arrangements: 6!/6! = 1
Ways to draw: 7*6*5*4*3*2 = 5040
Product: 5040

Case 2.
1 - Y
1 - W
4 - B

Arrangements: 6!/(1!1!4!) = 6*5 = 30
Ways to draw: 9*5*7*6*5*4 = 37800
Product: 1134000

Case 3.
2 - Y
2 - W
2 - B

Arrangements: 6!/(2!2!2!) = 6*5*3 = 90
Ways to draw: 9*8*5*4*7*6 = 60480
Product: 5443200

Case 4.
3 - Y
3 - B

Arrangements: 6!/(3!3!) = 2*5*2 = 20
Ways to draw: 9*8*7*5*4*3 = 30240
Product: 604800

Total Ways: 7,187,040

out of: 21*20*19*18*17*16 = 39,070,080

or about: 18.4% chance

it seems kinda low.....

Help!