jonlai9
12-01-2006, 12:31 AM
I want to find the probability of getting a straight out of 12 cards.
So for the denominator it is 52 nCr 12.
For the numerator... I know that there are 10 possible straights if I don't break up A and 2. Out of the 10 straights, I choose one. Then, I need to choose five corresponding cards out of 4 suits. I get this:
(10 nCr 1)*[(4 nCr 1)^5]
Finally, since I am choosing 12 cards, I need to choose 7 more cards out of the remaining 47 cards.
So the numerator would be:
(10 nCr 1)*[(4 nCr 1)^5]*(47 nCr 7)
And putting that with the numerator to get the probability, I would get:
(10 nCr 1)*[(4 nCr 1)^5]*(47 nCr 7)
-------------------------------------
(52 nCr 12)
But if I divide this, I get 3.xx... and probability should be 0 => 1.. what am I doing wrong?
So for the denominator it is 52 nCr 12.
For the numerator... I know that there are 10 possible straights if I don't break up A and 2. Out of the 10 straights, I choose one. Then, I need to choose five corresponding cards out of 4 suits. I get this:
(10 nCr 1)*[(4 nCr 1)^5]
Finally, since I am choosing 12 cards, I need to choose 7 more cards out of the remaining 47 cards.
So the numerator would be:
(10 nCr 1)*[(4 nCr 1)^5]*(47 nCr 7)
And putting that with the numerator to get the probability, I would get:
(10 nCr 1)*[(4 nCr 1)^5]*(47 nCr 7)
-------------------------------------
(52 nCr 12)
But if I divide this, I get 3.xx... and probability should be 0 => 1.. what am I doing wrong?