For the alphabet $\{0,1\},$ give a regular expression for each the languages described below. $$

a$.$ The language of all strings that begin with $10$ and end with $00.$

b$.$ The language of all strings that end with a $0.$

c$.$ The language of all strings such that every occurrence of $1$ is followed immediately by a $0.$

d$.$ The language of all strings that the number of changes from $0$ to $1$ is the same as the number of changes from $1$ to $0$ when read left to right. As an example, $00111011110$ is in the language since there are two places where $0$s change to $1$s and two places where $1$s change to $0$s; however, $0011101$ is not in the language since $0$s change to $1$s twice, while $1$s change to $0$s only once$)$