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Combinations

What about this one?

     You have 105 employees and you need to select a committee of
     3: a president, a secretary and a treasurer.  How many ways can
     you do it?

* Does order matter?  Totally!

Check it out:

Suppose that Bubba, Spike and Zeebo are the employees that get chosen...

     These are different:

Zeebo as president , Bubba as secretary , Spike as treasurer

Bubba as president , Spike as secretary , Zeebo as treasurer

So, let's do it with slots:

105 options for president * 104 options for secretary * 103 options for treasurer = 1,124,760

Notice that the arranging makes the number of ways a LOT higher.

 

YOUR TURN:

There are 15 kids and you need to pick 9 of them to help you T.P. a house.  How many ways can you do it?

 

There are 15 kids and you need to pick 9 to form a softball team.  You'll be assigning positions too.  How many ways can you do it?