My statistics homework comes in a software package from Hawkes Learning, the same people who wrote my statistics book (which is in my mom’s car at the soccer field).
I have a problem, and this is my last of two ‘strikes’ if I get it wrong - meaning I will have to re-do all of the problems I’ve done so far (they won’t be the same problems).
“How many ways can a person toss a coin 6 times so that the number of tails is between 3 and 5?”
Sounds easy, but I can’t seem to figure it out.
2^6=64 is about as far as I get on it…
I’ve tried the combination rule [nCr = n!/((n-r)!*r!) ], but i’m not getting anywhere…
The way I first learned the “combination rule” was just as you explained. I don’t know if your teacher/textbook mentioned this, but I’ve found it much more meaningful to think of nCr as “n choose r” (when order doesn’t matter).
So, 6C3 in your example is, “out of 6 tosses, how many ways to choose exactly 3 as tails.”
Another thing I didn’t learn/realize at first was that, instead of using the standard formula you have, it’s computationally simpler to compute, for instance, 6C3 as:
