I'm not really sure how to go about this, so any help would be greatly appreciated!
Suppose you throw a six-sided die five times. Find the probability that the sum of the outcomes of the throws is 15 using generating functions.
You can use:
When you expand it out, the coefficient of x^15 is your answer.
Doing so, we see the coefficient of x^15 is 651.
The total number of outcomes is
Therefore, the probability of getting a sum of 15 is
Oops, CB beat me. Oh well, same conclusion. That's good.
The thing to do is use a calculator that'll expand. But, if you must do it the long way.
We take note that we factored out a x^5. Therefore, we need only look for x^10 terms, instead of x^15.
When we multiply we get:
Looking at this we can see the terms:
are the terms which have the x^10 term when we multiply.