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

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) = (26"!")/(24"!") = 26 xx 25 = 650`
and three-digit number can be formed out of the 10 digits `= ""^(10)P_(3) = 10 xx 9 xx 8 = 720` ways
`therefore" "` Total number of licence plates `650 xx 720 = 468000`