Posted by **manny** on Tuesday, September 4, 2007 at 2:31pm.

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

- math -
**mathstudent**, Tuesday, September 4, 2007 at 4:51pm
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

- math -
**Anonymous**, Sunday, September 9, 2007 at 2:48am
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

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