Is my math correct?

[Calvenor]

Last few days I picked up a number of 8N dot coms, which I considered to be a nice catch and went on to reg them without thinking much (read: at all).

Now, doing some post-purchase validation and assessment of this investment (I know, should've done that before coughing up money), I tried calculating how many different combinations there are that meet the below three criteria:

1) each sequence consists of 8 digits (all numbers)
2) first digit is always an 8
3) each 8 digit sequence has exactly six 8's

Unfortunately it's been decades since my high school and uni courses in math and probability, so without remembering procedures and exact formulas I devised some semi-manual method that gave me final result of 1620 combinations total.

So, is that right, or I am way off? Math people, please lend your hand (and head) here.

 

[Michael R.]

I'm not very good at math, but I think our friend is here: https://en.wikipedia.org/wiki/Combination

You need first to compute the number of 2-combination for a set of 7 elements (since your first number is fixed and always 8).

Intermediate result is 21 (check here http://stattrek.com/online-calculator/combinations-permutations.aspx).
This is the number of combinations of 2 elements for a set of 7.

Then, for the first number, you have 9 possibilities (since you can't choose 8), and then again 9 for the second.

I think the final result is: 21 x 9 x 9 = 1701 combinations.

 

[Calvenor]

I'm not very good at math, but I think our friend is here: https://en.wikipedia.org/wiki/Combination

You need first to compute the number of 2-combination for a set of 7 elements (since your first number is fixed and always 8).

Intermediate result is 21 (check here http://stattrek.com/online-calculator/combinations-permutations.aspx).
This is the number of combinations of 2 elements for a set of 7.

Then, for the first number, you have 9 possibilities (since you can't choose 8), and then again 9 for the second.

I think the final result is: 21 x 9 x 9 = 1701 combinations.

I believe you are correct. I guess I used similar method, creating subsets of 7 digit sequences (because 8 is fixed in first position and doesn't attribute to any changes) and then multiplying total number of subsets by 81 (9 x 9 for all possible combinations of remaining digits in each subset).

Of course, doing things half-assedly I overlooked one subset and therefore instead of 21 x 81, which would've given me 1701, I counted with 20 alone and ended up with 1620 instead.

Your response made me go back to Excel file that I used for analysis and realize that I skipped one subset. Well, at least I was on right track

Thank you very much for your help