Recent content by psilentist

[solved] Okay, I realized what I was doing wrong. I had the right approach, but the condition we need to satisfy in order to use PIE is that each container contains GREATER THAN 6 objects, not greater than 5. That is, the die roll is greater than 6. (Then, by applying PIE, we find all...

oops... ci is x >= 6

How many sums with exactly one 4? I started working through the problem as you suggested, but it becomes pretty painful counting the possible combinations with exactly one 4. Permutations of 1 3 6 6, 2 2 6 6, 5 3 2 6, etc... With that many, how can you be sure you're covering all of them...

Homework Statement If you roll a fair die 5 times, what is the probability that the sum of the five rolls is 20? Homework Equations The Attempt at a Solution I know the sample space is all possible permutations of 1 to 6 taken five at a time with repetition, which is 6^5 = 7776...