posted by Hassan on .
In how many ways can a person choose 3 movies to see in a theater playing 11
Just start at the beginning and think it through choice by choice.
There are 11 to choose from. How many can you choose? 11.
Now you've seen one. Choose another. How many do you have to choose from? 10, 'cos you've already seen one.
So how many ways can we choose 2 movies from 11? If the order matters, as for example if you have to see Movie 1 before Movie 2: The Sequel, then there would be 11 * 10 ways, but from your question, that's not the case here, so seeing Movie 1, and then Movie 2, or the other way around counts as one case; both ways you've seen Movies 1 and 2. So we need to divide that 11 * 10 by (1 * 2) which are the number of orders in which we can see them.
For three movies, as can choose from 11, then 10, then 9, but again since order doesn't matter, we need to divide that answer by the number of orders in which we could see those movies, which is (1 * 2 * 3).