Australian AMC 2012 - Senior Question 18

Question 18

Jess marks four of eight identical cards with an $X$ and the other four with a $Y$. She shuffles them and puts them face down in a row and challenges Mike to guess the letter on each card. Mike decides to choose $XYXYXYXY$. What is the probability of Mike correctly guessing all eight cards?

$\frac48$
$\frac1{70}$
$\frac1{85}$
$\frac1{90}$
$\frac1{256}$