How many strings of eight English letters are there a) that contain no vowels, if letters can be repeated? b) that contain no vowels, if letters cannot be repeated? c) that start with a vowel, if letters can be repeated? d) that start with a vowel, if letters cannot be repeated? e) that contain at least one vowel, if letters can be repeated? f) that contain exactly one vowel, if letters can be repeated? g) that start with X and contain at least one vowel, if letters can be repeated? h) that start and end with X and contain at least one vowel, if letters can be repeated?

How many strings of eight uppercase English letters are there a) if letters can be repeated? b) if no letter can be repeated? c) that start with X, if letters can be repeated? d) that start with X, if no letter can be repeated? e) that start and end with X, if letters can be repeated? f) that start with the letters BO (in that order), if letters can be repeated? g) that start and end with the letters BO (in that order), if letters can be repeated? h) that start or end with the letters BO (in that order), if letters can be repeated?

How many license plates can be made using either two uppercase English letters followed by four digits or two digits followed by four uppercase English letters?

How many one-to-one functions are there from a set with five elements to sets with the following number of elements? a) 4 b) 5 c) 6 d) 7

In how many ways can a photographer at a wedding arrange six people in a row, including the bride and groom, if a) the bride must be next to the groom? b) the bride is not next to the groom? c) the bride is positioned somewhere to the left of the groom?