A movie theater offers 6 showings of a movie each day. A total of 1000 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. How many possibilities are there for the tallies for each showing for that day?

2.03 × 10¹⁴ different possibilities.

Step-by-step explanation:

We want to know the different ways 1000 people can come out to watch a movie at 6 different times of the day.

This is a permutation and combination problem.

Dividing 1000 people amongst 6 movie showings = 1005C5 = 1005!/(1005-5)!5!

= (1005×1004×1003×1002×1001×1000!)/(1000!5!) = (1005×1004×1003×1002×1001)/5! = 2.03 × 10¹⁴ different possibilities.