Question

How many automobile license plates can be made if each plate contains two different letters followed by three different digits?

Answer 1

We have 26 English alphabet and 10 digits (0 to 9)

Since, it is given that each plate contains 2 different letters followed by 3 different digits.

∴ Number of arrangement of 26 letters taken 2 at a time

= ²⁶P₂

= `(26!)/((26 - 2)!)`

= `(26!)/(24!)`

= `(26*25*24!)/(24!)`

= 650

 Three-digit number can be formed out of 10 digit = ¹⁰P₃

= `(10!)/(7!)`

= `(10*9*8*7!)/(7!)`

= 720

∴ Total number of license plates = 650 × 720 = 468000.