Example 1-1 Suppose a BASIC language restricts identifiers to a maximum of three characters, requiring the 1st character to be one of the 26 English letters, and the 2nd and 3rd characters can be English letters or Arabic numerals $0,1,2,3,4, \cdots$, 9. Find the number of identifiers.
Identifiers can consist of one character, or two characters, with a maximum of three characters.
A single character can only be one of the 26 English letters.
When two characters are used, the first character is one of the 26 English letters, and the second character can be one of the 26 English letters or one of the 10 Arabic numerals, totaling 36 possibilities. According to the multiplication rule, the number of two-character identifiers is
$$
26 \times 36=936
$$

For three-character identifiers, the first character has 26 possibilities, and the second and third characters each have 36 possibilities, so the number of three-character identifiers is
$$
26 \times 36 \times 36=33696
$$

According to the addition rule, the total number of identifiers with at most three characters is
$$
N=26+936+33696=34658
$$