How many license plates consist of 2 letters followed by 2 digits, if one of the digits must be odd and the other must be even, and the letters are different?
There are two cases; either the odd number comes first or the even number comes first.
Let's first deal with the case where there are two letters, then an odd number, than an even number.
There are 26 letters and 10 digits (0-9 where 5 are even and 5 are odd) so there are \(26*25*5*5=16250\) ways to do this.
The second case is the same thing, so we get \(16250\) again.
Therefore our answer should be \(32500\).