$1)$ Draw the state diagram for a DFA that recognizes the language L $=$ strings over $\{$b$,$c$\}$ that start with a b and contain an odd number of c$\text{'}$s$.$ Examples: bc$,$ bbcb$,$ bcb$,$ bccc$,$ bcbcbc$,$ bbbbccccc$.$

$2)$ Using the construction DFA $-->$ GNFA $-->$ regular expression, derive a regular expression that describes L $($from Question $1).$