The number of automobile license plates that can be made if each plate contains two different letters of English alphabet followed by three distinct digits,

Question:

The number of automobile license plates that can be made if each plate contains two different letters of English alphabet followed by three distinct digits, is_______.

Solution:

Each automobile license plates has 5 places to fill 2 places of alphabet (out of 26) can be filled in 26 × 25 ways 

Then 3 places of digits can be filled in 10 × 4 × 8 ways 

Hence number of different automobile license 

plates = 26 × 25 × 10 × 9 × 8 

= 468000

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