Counting Methods

Question

If you toss a coin 10 times and list the results (heads or tails) in order, how many different orders are possible?

Answer 1

Jesse,

 

Let's think about this one coin at a time...

 

- For a single coin, how many different possible results can you get?  Heads.  Tails.  That's two.

- For the second coin, you can still get two possible results.  So, for either of the two results in the first flip, I can get heads or tails for the second flip.  That's a total of 2x2, or 4 possibilities.  Here they are:

 

HH

HT

TH

TT

 

- For the third coin, I can take any of those first 4 orders, and then tack on a heads or a tails.  So, you end up doubling the list again.  That's 4x2, or 8 possible orders, after 3 flips.

 

If we keep going like this, and I flip it 10 times, then you get 2, x2, x2...for all 10 flips.  Just get the right number of 2's, and multiply them together correctly, and you'll have your answer.

 

Hope that helps!

 

Answer 2

Twenty different orders