asciijai wrote:The total number of outcomes will be 6^4 here.
so we have 4 places (4 rolls of the dice) and numbers 1,2,3,4,5 can be used to fill these 4 places
if I take that as 5C4 = 5 ways. Then these 4 selections will move around among themselves so it will be 5* 4! ways = 120 ways. How do I get ahead from here ?
You have two options.
1:: Find the number of INVALID possibilities, then subtract that from the total.
You saw that the total is 6�. You will get NO 6s in 5� possibilities. So you're left with 6� - 5� possibilities in which there is at least one six. This gives 6� - 5�, or (6² + 5²)(6² - 5²), or 61 * 11, or 671.
2:: Find the number of VALID possibilities, case by case.
Exactly one 6 = 1 * 5 * 5 * 5 * 4 (since any of the four dice could be the 6)
Exactly two 6s = 1 * 1 * 5 * 5 * 6 (since any two of the four dice could be 6, and (4 choose 2) = 6)
Exactly three 6s = 1 * 1 * 1 * 5 * 4 (since any three of the four dice could be 6, and (4 choose 3) = 4)
All 6s = 1 * 1 * 1 * 1
This sum is 4*125 + 6*25 + 20 + 1, or 671.
