Question

a movie theater has 14 different movies showing. If you want to attend no more than 3 of the movies, how many different combinations of movies can you attend

Answer 1

14C3 = 14! / 11!3! 

= 14 x13 x12 / 3x2x1 
= 2184 / 6 
= 364 different combinations 

The first movie can be any of 14 
As you have already seen one the second movie can be any of the 13 remaining 
As you have already seen two the third movie can be any of the 12 remaining. 

Therefore there are 14 x 13 x 12 = 2184 PERMUTATIONS of movies you can see. 
However among those 2184 different permutations will be instances where you have watched the same three movies but just in a different order. 
eg ET, The Piano, Harry Potter = ET Harry Potter The Piano = The Piano, ET, Harry Potter = The Piano Harry Potter ET = Harry Potter ET The Piano = Harry Potter The Piano ET. 
For each set of three films there are 3! or 3x2x1 or SIX different ways they can be arranged in. 
Therefore we need to DIVIDE the above 2184 permutations by 6 to get the number of COMBINATIONS of different films that can be watched. 
2184 / 6 = 364