Youth Boys

There are 6 boys and 8 girls in a youth group. What is the probability of the following events?

a) Picking a committee of 4 consisting of 1 boy and 3 girls.
b) Picking a committee of 6 consisting of 3 girls and 3 boys.
c) Picking a committee of 5 consisting of at least 4 girls

I seem to be going in the right direction, as i'm getting the denominator correct, however i cannot manage to get the numerator right.

The answer is 336/1001 (or 48/143 reduced). I cannot manage to get the steps right though.

a) (6C1)(8C3)/(14C4) = (6)(56)/(1001) = 336/1001 = 48/143 = .3356643357

b) (6C3)(8C3)/(14C6) = (20)(56)/(3003) = 1120/3003 = 160/429 = .372960373

c) [(6C1)(8C4) + (6C0)(8C5)] / (14C5) = [6(70) + 1(56)] / 2002 = 476/2002 = 34/143 = .2377622378

1 Iran China Asian Youth Boys Volleyball Championship والیبال ایران چین