Using the digits {2, 3, . . . , 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

Using the digits {2, 3, . . . , 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.