I am asked N>=3 sets of dice are thrown. How many way can exactly 3 sixes turn up.
I did the following
for a single set of dice....
dice1+dice2=6 how many solutions?
(5 choose 1)/2ceiling function??? which is 3 ways
so for 3 dice to roll 6 there are...
then the other n-3 dice can roll anything but a six.
so there are 18 unique ways to roll a set of dice
18-3=15 -the total ways to roll a dice with no 6.
so I get...
Now my big problem is how do I express this answer in terms of binomial co-efficient?