Hello. I am not a math major, just a math tutor. I haven't taken anything beyond Calculus I, but even then my calculus is rusty. Enough about me, now for my problem.
I hope this belongs here and not in the pre-university threads. It doesn't seem elementary to me, but I am hoping I can be proven wrong.
Recently, a friend provided me with this formula:
With it, I can derive the probability, P, of reaching a sum, p, when rolling a certain number of dice, n, each with the same number of sides, s.
For example, the odds of reaching a sum p=19 for n=6 dice each with s=6 sides are 3,906 out of 46,656.
It's the next step with which I am having trouble (and is actually my question).
How do I calculate the odds of reaching a sum of 19 rolling six 6-sided dice when I disregard the die showing the lowest value? the highest value? the two lowest values? etc.
How do I calculate the odds of reaching any sum, p, rolling n s-sided dice when I disregard one or more dice based on their comparative values?
Thanks in advance for the help. I hope this doesn't prove impossible.
Oh. I don't want to write out all the combinations by hand. I want to use a formula perhaps like the one above, not a computer program which does the calculation for me.