selfmade wrote: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, for each value from 1 to 6, there are two cards in the deck with that 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
My method might be a bit lengthy. But I would still post it
We need to find the chance for atleast one pair.
I am finding the chance for no pair.
We need to pick 4 cards from 2 sets of 6 each.
This can be doen in:
All 4 from first set = 6c4 = 15 ways
3 from 1st set and 1 from second set = 6c3 * 3c1 =60 ways (3C1 Because, the pairing cards should not be chosen)
2 from 1st set and 2 from second set. = 6c2 * 4c2 = 90 ways
1 from first set and 3 from second set = 6C1 * 5c3 = 60 ways
All 4 from second set = 6c4 = 15 ways
Hence total = 240.
Now, total number of ways of choosing 4 cards from the 12 cards is 12c4 = 495
Hence chance of getting atleast 1 pair = 1-(240/495) = 17/33
Hope this helps!!
"Once you start working on something,
don't be afraid of failure and don't abandon it.
People who work sincerely are the happiest."
Chanakya quotes (Indian politician, strategist and writer, 350 BC-275BC)
