Discrete Mathematical Structures by Pearson

5-4 Discrete Mathematical Structures

How many distinct plates can be printed if

(1) repetition of letters and digits are allowed.

(2) only letters can be repeated.

(3) only digits can be repeated.

(4) neither letters nor digits can be repeated.

Solution: The number of license plates that can be printed are

(1) 26 × 26 × 10 × 10 × 10 = 676 × 10

3

(2) 26 × 26 × 10 × 9 × 8 = 676 × 720

(3) 26 × 25 × 10 × 10 × 10 = 65 × 10

4

(4) 26 × 25 × 10 × 9 × 8 = 650 × 720 = 468 × 10

3

Example 5 How many five-digit telephone numbers are possible if (1) only even digits are used

and (2) only odd digits are used.

Solution:

(1) The even digits are 2, 4, 6, ...