I have a 42 card deck. I have 3 copies of card #1 in the deck, and 10 copies of card #2 in the deck.
I just really want to know what the probability is (in a ratio, fraction, or percentage) that I would get 1 copy of card #1 and 2 copies of card #2 in my hand. Oh, and the hand is 6 cards. the other three cards in the hand don't matter.

"all the combinations of 6 cards from 42 = 42C6 = 5245786

all the combinations of 1 card#1 from 3 = 3C1 = 3
all the combinations of 2 cards#2 from 10 = 10C2 = 10! / (2! x 8!) =45
all the combinations of 3 cards from 29 cards ( 42 - (3 + 10) ) = 29C3 = 29! / (3! x 26!) = 3654

probability = 3 x 45 x 3654 / 5245786 = 0.094035 = 9.4 %