There are [tex]\binom{52}4[/tex] ways of drawing a 4-card hand, where
[tex]\dbinom nk = \dfrac{n!}{k!(n-k)!}[/tex]
is the so-called binomial coefficient.
There are 13 different card values, of which we want the hand to represent 4 values, so there are [tex]\binom{13}4[/tex] ways of meeting this requirement.
For each card value, there are 4 choices of suit, of which we only pick 1, so there are [tex]\binom41[/tex] ways of picking a card of any given value. We draw 4 cards from the deck, so there are [tex]\binom41^4[/tex] possible hands in which each card has a different value.
Then there are [tex]\binom{13}4 \binom41^4[/tex] total hands in which all 4 cards have distinct values, and the probability of drawing such a hand is
[tex]\dfrac{\dbinom{13}4 \dbinom41^4}{\dbinom{52}4} = \boxed{\dfrac{2816}{4165}} \approx 0.6761[/tex]
