So suppose you have a fair six sided die, i want to know how to Calculate the probability of choosing 3 numbers then rolling a die 3 times and receiving the same 3 numbers that were previously chosen in any order. How would i do this using combinations?
At this stage i was thinking something along the lines of 6C3+6C3+6C3 but that doesn't really get me anywhere.
If the numbers you are choosing are distinct, the total number of permutations of your 3 numbers is $3^3 = 27$. The total number of outcomes of 3 rolls of a dice is $6^3 = 216$. So the probability that your 3 numbers appear (in any order) is $27/216 = 1/8$.