Passwords for a certain computer system are strings of uppercase letters. a valid password must contain an even number of x’s. determine a recurrence relation for the number of valid passwords of length n. note: 0 is an even number, so abbc is a valid password. this counting problem is pretty tricky. here’s a good way to think about it: to make a good password of length n you can either (a) add any non-x to the end of a good password of length n − 1, or (b) add an x to the end of a bad password of length n − 1. for (b) you can use the good = total-bad trick to count the number of bad passwords of length n−1.