[1] Agree...that was never in dispute...
[2] that's for a total of 99,532,800; Pka's is 2,073,600
Soooo....what can I say?:cool:
Btw, I'm not picking sides or calling anything correct or incorrect;
I'm trying to understand/follow what is going on...
Denis,
Why do you think I started out with "Now admittedly I don't always do too well on some types of permutations/combinations ...". I'm willing to be convinced. Besides, that 99 532 800 is before duplicates are removed and that's generally where I get caught up.
Take a simple example of choosing any two cards from a deck of 52. First card is 52 choices and second card is 51 choices so there are 2652 ways to chose, right? Well, maybe; is the A of Spades, King of Hearts considered the same as the King of Hearts, Ace of Spaces? If the answer to that question is no, then the 2652 is correct and we are talking about permutations. However, if the answer is yes, they are considered the same, the number has to be reduced by the number of 'duplicates' and we are talking about combinations. In the simple example here, the ways you can arrange the two cards is 2!, so divide the 2652 by 2! to get 1326 ways.
In that sense, my 99 532 800 would have to be divided by 8!. However, that does not give a whole number so that must be incorrect. Where is it wrong? I don't know. That's why I didn't go any further and just said we had to remove the duplicates. Maybe I only have to divide by 4! since we only have 4 'sets'; 1 trips, 2 pairs, and 1 single? Or maybe the 4 sets and the arrangement of the two pairs, i.e. 4! * 2!. That latter would actually make my answer and pka's answer the same as the difference between the permutation number of 99 532 800 and pka's 2,073,600 is 48 = 4! * 2!
Edit to correct the spelling of "pka's" - sorry 'bout that pka