Ordering three second-moment quantities for dice

Throw a fair die five times independently, with results $X_1,\dots,X_5$, and let $M$ be their median (the third smallest). Consider three quantities: (a) the expected product of the first two results, $\mathbb{E}[X_1 X_2]$; (b) the expected square of the first result, $\mathbb{E}[X_1^2]$; (c) the expected square of the median, $\mathbb{E}[M^2]$. Order them from largest to smallest and report the order as a three-digit number using $a=1$, $b=2$, $c=3$ (so $321$ would mean $c>b>a$).

$231$. Independence gives (a) $=3.5^2=12.25$, and (b) $=\tfrac{91}6\approx15.17$. The median has mean 3.5 but is more concentrated than a single roll, so its second moment sits between the two: (c) $=\tfrac{2207}{162}\approx13.62$. Thus $b>c>a$.