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 ___________.

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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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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 ___________.

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

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