Garage Sale!
I have a collection of nine movies which come from three different trilogies. How many distinct non-ordered groups of movies can I take from my collection such that no three movies come from the same trilogy?
Note: A group can have any whole number of movies.
The answer is 343.
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
Let the movies be a 1 , a 2 , a 3 , b 1 , b 2 , b 3 , c 1 , c 2 , c 3 where a , b , c represent different trilogies.
For the group a 1 , a 2 , a 3 , we can make 8 distinct subsets, but one of them is not possible since it contains all 3 movies from the same trilogy, so we can make 7 possible subsets from here.
Similaly, there are also 7 subsets possible for b and c . We just multiply the number of possible subsets for the trilogies, i.e. 7 3 = 3 4 3 .