What is the Probability that the Lowest Card out of 4 Cards is X? If I have four different value cards, what is the probability that the lowest card (ace, lowest -> king, highest) is some value X?
Here is what I have so far:
I know that the lowest value card cannot be a king, queen, or jack, as there must exist a value that is 3 above. And I can guess that the probability of an ace will be the highest and a 10 will be the lowest. Can someone please give me some hints on how I should approach this?

HINT: Since you’re looking at sets of $4$ cards of different denominations, you might as well just look at sets of denominations: in effect you’re choosing $4$ cards from one suit and asking for the probability that the lowest denomination chosen is $x$. There are $\binom{13}4$ possible sets of $4$ denominations. How many have an $x$ as lowest denomination? You must choose the other $3$ from how big a set of values?
