In the small country of Ruritania, car registration plates consist of different arrangements of groups of 4 letters taken from the Ruritanian alphabet which
consists of 10 letters. Calculate the number of different registration plates which
can be made if
(a) repetitions of letters are not allowed
v
(b) the letters can be repeated any number of times
In case (b), all the different possible arrangements are listed and one
arrangement is then to be chosen at random. Calculate the probability of
choosing an arrangement which has
(c) two or more letters the same
(d) different letters at the beginning and the end of the arrangement.