Suppose we're dealt a 7 card hand from a standard 52 card deck. I'm trying to find the probability that all 7 cards are different ranks (that is, no two cards share the same rank).
I know the denominator in this will be 52C6, but I'm not as sure on the numerator.
I was thinking the first card doesn't matter (it's always unique), so something like:
48 * 44 * 40 * 36 * 32 / 52C6
Thoughts?
Thanks,
Mariogs
Best Answer
There are ${ 52 \choose 7}$ ways of picking a 7 card hand from a deck of 52. I think that is the denominator, not ${52 \choose 6}$. Now, you can pick 7 different ranks ${13 \choose 7} $ ways, and each could be 1 of 4 possible suits. Therefore, the probability should be $\frac{{13 \choose 7} \times 4^7}{{52 \choose 7}} = 0.21$