Hello, thank you in advance for help here. I am just trying to figure this out for my own edification. If I took 6 dice, each a regular 6 sided cube, how many possibilities are there of me rolling a four of a kind and a two of a kind? In other words, rolling a 646646, 222112, 333344, any abaaba series of numbers?
A four of a kind is nothing more than 6C4, then you multiply that by 6 for each possibility, then 5 for each roll that is not the same as the four of a kind, and then multiply that by four, to account for the rolls that are not the same as the four of a kind or the first "odd dice out".
The Attempt at a Solution
I got that problem right, 6C4*6*5*4, or 1800. If you account for the number of possibilities of any roll, 6^6, the odds are 1800/46,656, but I cannot figure out how to go from that answer to getting a roll of a four and two. All help is appreciated, thank you.