Standard automobile license plates in a country display 2 nu

Standard automobile license plates in a country display 2 numbers, followed by 2 letters, followed by 3 numbers. How many different standard plates are possible in this system? (Assume repetitions of letters and numbers are allowed.)

Solution

The counting principle say that we multiply the number of ways for each of these events together to get the total number of ways to get a license plate.
.
number of ways to get the 1st number (the digits 0 through9): 10 ways (Assume lead 0 is allowed)

number of ways to get the 2nd number (the digits 0 through9):10 ways

number of ways to get the first letter: 26 ways
number of ways to get the next letter (repetitions OK): 26 ways

number of ways to get the next number (0 is OK): 10 ways
number of ways to get the next number (0 is OK): 10 ways
number of ways to get the next number (repetitions OK): 10 ways

.
Total number of ways to get a license plate:
10*10*26*26*10*10*10
.
There are \"67600000\" ways to create a license plate in this system.

if 0 is not allowed in 1st no

then 9*10*26*26*10*10*10 = 60840000