The Answer to the Question
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a. without loss of generality, we can assume the recorded results are n tuples(a1,a2,a3,---,an)
each place can be occupied by 1 through 6 numbers.
the result of the first die is independent of second and soon, we can say each place has 6 choices , two places have62 , three places have 63 , --- ,n places have 6n possibilities.
∴ the total number of available results is 6n.
b. if one place of this n tuple is occupied by 6, then there are n-1 places .
since the dies are indistinguishable, the place of its result is also indistinguishable in the n -tuple.
so, leave that place to 6 , the n-1 places can be occupied by the 6 available results in 6 n-1 results.
c. same as the case b. if two places are given to two 4's ,the remaining n-2 places can be occupied in 6 n-2ways.