### Instruction: 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?### Response: I need to find the total number of possible license plates that fit the given criteria.
To do that, I can use the multiplication principle, which says that if there are m ways to do one thing and n ways to do another thing, then there are m times n ways to do both things together.
In this case, the first thing is choosing 2 letters, and the second thing is choosing 2 digits with the given restrictions.
How many ways are there to choose 2 letters?
Well, there are 26 letters in the alphabet, and I can repeat them, so I have 26 choices for the first letter and 26 choices for the second letter.
That means there are 26 times 26, or 676 ways to choose 2 letters.
How many ways are there to choose 2 digits, if one must be odd and the other must be even?
Well, there are 5 odd digits (1, 3, 5, 7, 9) and 5 even digits (0, 2, 4, 6, 8), so I have 5 choices for the odd digit and 5 choices for the even digit.
But I also have to consider the order of the digits, since it could be odd-even or even-odd.
So I have to multiply by 2 to account for the two possible orders.
That means there are 5 times 5 times 2, or 50 ways to choose 2 digits with the given restrictions.
Now, to find the total number of possible license plates, I just multiply the number of ways to choose 2 letters by the number of ways to choose 2 digits.