Problem Solving

Bill has a small deck of 12 playing cards made up of only 2 suits of 6 cards each. Each of the 6 cards within a suit has a different value from 1 to 6; thus, there are 2 cards in the deck that have the same value.
Bill likes to play a game in which he shuffles the deck, turns over 4 cards, and looks for pairs of cards that have the same value. What is the chance that Bill finds at least one pair of cards that have the same value?
a) 8/33
b) 62/165
c) 17/33
d) 103/165
e) 25/33

Please explain how to approach such questions, I am having a tough time with them.

OA :
c

do it as 1-(Prob of not getting the cards)

Probability of picking first: 1 (because it can be any card)
2nd card not pairing: 10/11
3rd card not pairing : 8/10
4th card not pairing: 6/9

1*(10/11)(8/10)(6/9) = 16/33 (probability of no pairs)

1 - (16/33) = 17/33

Probability of at least one pair is 17/33


hope it helps....


MY GMAT IS TOMORROW PLS PRAY FOR ME!!!!!!

Thank you very much shibal.Wish you a very good luck.
You have a very sound skills and I am sure victory will be yours .
Just stay cool, calm and composed.