Using the digits 2 through 8, find the number of different 5-digit numbers such that: (a) Digits can be used more than once. (b) Digits cannot be repeated, but can come in any order. (c) Digits cannot be repeated and must be written in increasing order. (d) Which of the above counting questions is a combination and which is a permutation? Explain why this makes sense.

Please help explain for me. This question is confusing. If possible, please type answers. Thank you very much.  (1) Think about the three-digit numbers that can be formed from the digits 1, 2, 3, 4and 5 without repetition.(a) How many of these are there?(b) How many of them are even?(c) How many of them are greater than 250? (2) Some of these are partitions and some aren’t. You don’t need to find the answer, youjust need to say why it is or isn’t a partition.(a) Breaking this class up into first-year students, second-year students, etc.(b) Breaking this class up into CS majors, math majors, etc.(c) Splitting up the numbers {1, 2, . . . 10} into even and odd(d) Splitting up the numbers {1, 2, . . . 10} into multiples of three, multiples of two,or neither

A group of 8 people, including Betty and Bob, are going to take a group photo. In how many ways can they line up, order counting, if Betty and Bob must stand next to each other?    ___________

Clear steps please!