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

Answer

15552

Explanation

There are 26 English alphabets and 10 digits (0 to 9).
Since, it is given that each plate contains two different letters followed by three different digits.
`therefore` Arrangement of 26 letters, taken 2 at a time `= .^(26)P_(2)`
`=26xx25`
=650
And arrangement of 10 digit taken three at a time `= .^(10)P_(3)`
`=10xx9xx8`
=720
`therefore` Total number of license plates `=650xx720=468000`