Formulas to display all 3 letter combinations in 8 letters

[Mally]

I do a tote in my local club where I pick three letters for 10 pence. If
these come out I win several hundred pounds.

I have a spreadsheet that uses the FACT function to show the factorial of a
number up to the number 26 containing combinations of 3 numbers and the cost
e.g. 4 = 4 combinations of 3 numbers, 7 = 35 combinations of 3 numbers, 15
= 455 combinations of 3 numbers, etc., etc.

We pick 15 letters (instead of numbers) from 26 which costs £45.50 as there
is 455 combinations of 3 letters in 15.

We have been told that the most number of letters we can put on at once is 8
at a cost of £5.60 (56 combinations) but there is no limit to the number of
sets of 8 letters we can put on.

I know that there are, for example 56 combinations of 3 letters in 8
letters. How do I show how many sets of 8 letters there are that will cover
all of the 3 letter combinations from the 15 letters we pick?

We may pick different letters every time.

The total number of letters we pick may change but it will always cost 10
pence for 3 letters. It doesn’t have to be sets of 8 letters to cover the 15
letters (or the number selected).

If this can’t be done in excel is there any software out there that will do
it.

I hope this makes sense!

Thank you in advance for your help.

 

[Dana DeLouis]

Hi. I'll give it a try. I'm not sure of how the price is involved, so
I'll just stick to this part...

How do I show how many sets of 8 letters there are that will cover
all of the 3 letter combinations from the 15 letters we pick?

If I understand the question, it should be...

=COMBIN(15-3,8-3)
=792

I have a spreadsheet that uses the FACT function

Just to add in case you are not using it...
=COMBIN(8,3) = 56


If you are interested... my original equation was...
=HYPGEOMDIST(3,8,3,15)*COMBIN(15,8)

But you will notice that the denominator of HYPGEOMDIST cancels out the
Combin function. The first part of the remaining function cancels since

Combin(3,3) reduces to 1. What's left is the above equation.

- - -
HTH :>)
Dana DeLouis