Using Anagram - Need Help

[trangle.nh]

Hey,

I have some problems with anagram as follow:

Ex 1: If seven people board an airport shuttle with only three available seats, how many different seating arrangements are possible? (Assume that three of
the seven will actually take the seats

For this: we may use Anagram as follows: 123SSSS --> No of arrangement = 7!/4!

How can we deal with the following:

Ex 2: If 3 people board an airport shuttle with 7 available seats, how
many different seating arrangements are possible?

Please solve the problem with Anagram??

I know that we may use Slot method with these: 7x6x5 = 210

But how can we express it with Anagram: 123SSSS? ( before we use 123SSSS since there are 7 seven people, then how can we use 123SSSS when we have only 3 people)

General Question: How many letter are there in the ANAGRAM?
+ Depend on number of items in the pool?
+ Depend on the number of selected item?
+ Depend on larger number of the two above number?


Thanks!

[gmatboost]

In order to use the method you want to use you need to think of it 7 seats choosing among 3 people, because we need n (the total number of objects) to be >= k (the number of objects being chosen).