Can someone show me how to solve this problem using factorials?
I seem to be struggling w combination problems largely in deciding what the best method of answering the question is and how to proceed (which is probably a product of my lack of understanding combination stuff in general). In retrospect I see that it makes sense to use the 'slot method' and to also find the probability of there NOT being any pairs. So basically:
(12/12)*(10/11)*(8/10)*(6/9)=16/33 and 1-16/33= 17/33 or C.
But I feel like I should be able to get to this same answer using some combination of x!/(x-n)!n! or something. Appreciate any help.
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?
8/33
62/165
17/33
103/165
25/33
I seem to be struggling w combination problems largely in deciding what the best method of answering the question is and how to proceed (which is probably a product of my lack of understanding combination stuff in general). In retrospect I see that it makes sense to use the 'slot method' and to also find the probability of there NOT being any pairs. So basically:
(12/12)*(10/11)*(8/10)*(6/9)=16/33 and 1-16/33= 17/33 or C.
But I feel like I should be able to get to this same answer using some combination of x!/(x-n)!n! or something. Appreciate any help.
