Question

Suppose a code consist of two letters followed by a digit. Find the number of

(a) Codes

(b) Codes with distinct letters

(c) Codes with the same letters

Answer 1

Assuming there are 26 letters (no distinction among case) and 10 digits:

A) 26 * 26 * 10 = 6760
B) 26 * 25 * 10 = 6500
C) 26 * 1 * 10 = 260

Answer 2

a) Codes
The way of labeling a code with two letters followed by a digit
Assigning one of the 26 letters: A, B, C, D…., F
Assigning one of the 10 digits: 0, 1, 2…, 9
There are two letters so 26
By product rule there are 26×26×10 = 6760 codes

b) Codes with distinct letters
The way the distinct letters are label
25 character of first letters and 25 characters for the second letter so
There are 26×25×10=6500 codes

c) Codes with same letters
The way the same letters are label
26×1×10=260 codes