Please answer all of question 2 (2.a, 2.b, and 2.c) , and please include not only a mathematical answer, but some explan

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Please answer all of question 2 (2.a, 2.b, and 2.c) , and please
include not only a mathematical answer, but some explanation as to
why this is the case:
2.a) If "n" balls are randomly placed into "n" cells (so that
more than one ball can be placed in a cell), what is the
probability that each cell will be occupied?
2.b) A fair die is tossed 8 times. What is the probability of
exactly two 3’s, exactly three 1’s and exactly two 6’s?
2.c) Show that the probability of an even number of Heads in "n"
tosses of a fair coin is always 1/2.