Redo Problem P3 2 for a license plate that has two digits followed by three uppercase letters A to Z

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

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.

Concept: Derivation of Formulae and Their Connections

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