Permutations or Combinations or some other function??

[Mark Siler]

I'm trying to figure what function I need to use. I unerstand that when
order does matter I should use Permutations and Combinations when it
doesn't. For example if I want to know how many two letter group I can make
from the word CAT and order does not matter I'd use Combinations and the
results would be CA, CT and AT. But here's my question, what if I needed to
know how many different Combinations I could have from three blank spots to
all letters. On something small I like CAT I can just write them out.

CAT
CA_
CT_
AT_
C_ _
A_ _
T_ _
_ _ _

COMBIN does't work. The first number I'd enter for the formula would be the
total number of letters, in this case 3. The next number is the number of
groups and this is what seems to be the issue. I got the right answer when I
did =COMBIN(3,3)+COMBIN(3,2)+COMBIM(3,1)+COMBIN(3,0), but what do I do if I
have 15 letters. The must be a function that does this that I'm not
finding??

Thanks,
Mark

 

[Guest]

Hi,

Try this formula:

N+2+(N*(N-1)/2)

Where N stands for number of letters.

Regards,

Jaleel

 

[Mark Siler]

The proposed formula doesn't work. If you have 4 letters the formula returns
12 when the answer should be 16. I've figured out that if you list the
number of letters as binary. 64 32 16 8 4 2 1
where counting from the right each place is the number of letters. If there
are 4 letters then it would be 8 4 2 1 and if you add up all the
number in this case you get 15 then add one for the options of where places
are empty. This is how I figured it was 16 for 4 letters. 5 letters would
be 16+8+4+2+1+1=32. I'm still looking for a formula that will do this???

 

[Dana DeLouis]

Hi. I believe you are looking for the number of Subsets, which as you
mentioned, does include an empty set.
2^n

http://mathworld.wolfram.com/Subset.html

 

[Mark Siler]

You are correct Dana.

Thank you and Happy Holidays!
Mark