A movie theater offers showings of a movie each day. A total of 500 people come to see the movie on a particular day. The theater is interested in the number of people who attended each of the six showings. 81 +82 +83 +84 +85 +86 = 500. How many possibilities are there for the tallies for each showing for that day if... a ... there are no restrictions? b ... none of the showings can be an empty theater? c...81 2, 82 ≥3, 83 4, 84 ≥5, 85 ≥6, 86 ≥ 7?

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