Given $a = 6$, $b = \frac{20}{3}$, $c = 2\sqrt{10}$, and $d$, where $d$ is a rational number. These four numbers are marked on a number line as $A(a)$, $B(b)$, $C(c)$, and $D(d)$. Select the correct options. (1) $a + b + c + d$ must be a rational number (2) $abcd$ must be an irrational number (3) Point $D$ could possibly be at a distance of $2\sqrt{10} + 6$ from point $C$ (4) The midpoint of points $A$ and $B$ is to the right of point $C$ (5) Among all points on the number line at a distance less than 8 from point $B$, there are 14 positive integers and 1 negative integer
Given $a = 6$, $b = \frac{20}{3}$, $c = 2\sqrt{10}$, and $d$, where $d$ is a rational number. These four numbers are marked on a number line as $A(a)$, $B(b)$, $C(c)$, and $D(d)$. Select the correct options.
(1) $a + b + c + d$ must be a rational number
(2) $abcd$ must be an irrational number
(3) Point $D$ could possibly be at a distance of $2\sqrt{10} + 6$ from point $C$
(4) The midpoint of points $A$ and $B$ is to the right of point $C$
(5) Among all points on the number line at a distance less than 8 from point $B$, there are 14 positive integers and 1 negative integer