Probability of choosing two random cards of the same value I know this question was asked here: What is the probability of choosing two cards of the same value?
But I'm trying to understand it in terms of combinations.
Two cards are randomly chosen from a deck of 52.  What is the probability that they have the same value?
I'm thinking:
$\frac{\binom{13}{1} \binom{3}{1}}{\binom{52}{2}}$
Out of 13 possibilities you choose the first card (say it's a 7).  Then for the second card you need to pick another 7 out of the remaining three 7's.
Can anyone explain to me where I'm going wrong in my thinking?
Thanks

When calculating probabilities for drawing without replacement it is better to treat the draws in sequence, so instead of $\binom{52}2$ in the denominator you have $52×51$.
The first factor in the numerator is $52$ since one card doesn't constrain the possibility of both cards having the same value. The second factor, for the second draw, is $3$ since that is the number of remaining cards sharing a value with the first draw. Thus we have $\frac{52×3}{52×51}=\frac1{17}$.
