math
posted by manny .
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

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 
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
Respond to this Question
Similar Questions

math
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. 
probability
you are to set up a code of consisting of three letters (A to Z) and five numbers (0 to 9). a) how many codes are possible if the letters and numbers can be repeated? 
Math
An identification code is to consist of six letters followed by three digits. How many different codes are possible if repetition is permitted? 
Math
1.) A security code has seven characters. Each code begins with two digits, then two letters, and finally three digits. the number of distinct security codes possible if repetition is allowed? 
gemetry
An identification code is to consist of two letters followed by six digits. How many different codes if repetition is permitted. 
Math110
how many 6  slots codes can be made up using 2 letters followed by 2 digits followed by 2 letters where All of the following conditions must be met: a. the allowable letters are A through G b. the allowable digits are 2 through 7 … 
math please hurry
A secret code must consist of three capital letters followed by a digit. Letters cannot be repeated. How many secret codes are possible? 
math30
A security code used to consist of two odd digits, followed by four even digits. To allow more codes to be generated, a new system uses two even digits, followed by any three digits. If repeated digits are allowed, the increase in … 
Discrete Math
Each Student at a certain university is given a 6digit code (such as 123789 or 001122) (a) how many different codes are there? 
Math
How many 3 letter security codes can be made from the 4 letters A,B,C,D?