Which of the following is a correct way to declare a variable in C?

Declaring a variable in C requires following specific naming conventions and syntax. The declaration of the variable using the syntax char name[]; is valid because it is a proper way to define an array of characters. In C, character arrays are commonly used to represent strings, and the notation name[] indicates that name is an array without an explicit size given at that declaration point, which is acceptable in certain contexts, particularly when declaring to initialize later.

The other choices presented violate C's variable naming rules. For instance, beginning a variable name with a number or including special characters like '$' is not permitted. Similarly, 'string' is not a built-in data type in C but is rather from C++, which further disqualifies that option.