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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