6 The length, $X$ centimetres, of worms of a certain type is modelled by the probability density function

$$f ( x ) = \begin{cases} \frac { 6 } { 125 } ( 10 - x ) ( x - 5 ) & 5 \leqslant x \leqslant 10 \\ 0 & \text { otherwise } \end{cases}$$

(a) State the value of $\mathrm { E } ( X )$.\\

(b) Find $\operatorname { Var } ( X )$.\\

(c) Two worms of this type are chosen at random.

Find the probability that exactly one of them has length less than 6 cm .\\

\hfill \mbox{\textit{CAIE S2 2020 Q6}}