Possible Combinations

[chooey]

Hi,

I am trying to find the number of pssoible combinations for this. There are 15 digits per combination and there are 2(X,O) per selection. Order is important.

Eaxmple:
XXXXXXXXXXXXXXX
XOXXXXXXXXXXXXX
XOOXXXXXXXXXXXX
XOOOXXXXXXXXXXX
OOOXXXXXXXXXXXX

Any help would be great. I used this forumla and wasn't sure if it is correct seems high. 2^15

Thanks

 

[JeffM]

Hi,

I am trying to find the number of pssoible combinations for this. There are 15 digits per combination and there are 2(X,O) per selection. Order is important.

Eaxmple:
XXXXXXXXXXXXXXX
XOXXXXXXXXXXXXX
XOOXXXXXXXXXXXX
XOOOXXXXXXXXXXX
OOOXXXXXXXXXXXX

Any help would be great. I used this forumla and wasn't sure if it is correct seems high. 2^15

Thanks

2^15 is correct.

The word digits is a bit deceptive. You do not mean digits; you mean symbols.

How many different strings can be formed with 15 places using one of two distinct symbols in each place?

Think about a simpler problem. Say there were three places.

xxx
xxo
xox
xoo
oxx
oxo
oox
ooo

That is all there are, and there are 8 = 2^3.

Let's try four places.

xxxx
xxxo
xxox
xxoo
xoxx
xoxo
xoox
xooo
oxxx
oxxo
oxox
oxoo
ooxx
ooxo
ooox
oooo

There are 16 = 2^4 of them.

Why does that formula work?

You have two choices for the first place, two choices for the second place, etc etc.

So with n places you have 2 * 2 ... = 2^n choices to make.

Make sense?