patrickmhoy wrote:
What is the rule for this type of combination problem? It doesn't seem to follow the fundamental counting rule (n!)/[(r!)(n-r)!].... or does it?
The first thing in Combinatorics is to figure out whether the problem is of Permutation or Combination.
This problem asks for the
"arrangement", so this is clearly a Permutation problem. But the author also says that one type of movie (Drama) has to be watched thrice.
So possible arrangements are -
DDDAC
ADDDC
ACDDD
DDACD
...
..
and so on.
Now you should see here that the 3 Ds are same, so their arrangement, when they are placed together, doesn't really matter.
So, like Bunuel has mentioned in the official solution, the total number of arrangements for n objects with repetition, in which object-1 repeats n
1 times, object-2 repeats n
2 times, object-3 repeats n
3 times and so on, can be given from the formula -
n!/(n
1! *n
2! * n
3! .....)
= 5!/(3! * 1! * 1*)
= 5!/3!
= 20
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