A die is rolled three times. What is the probability of obtaining three
even numbers ?
I've solved this problem calculating the number of total results:
$$u=D'_{6,3}=6^3$$
and the number of favorable results:
$$f=D'_{3,3}=3^3$$
I've got:
$$p=\dfrac{f}{u}=\dfrac{3^3}{6^3}=\dfrac{1}{8}$$
This result is correct.
If i try to calculate $u$ and $f$ as combination with repetition, i get an error
Is it not possible to solve this problem with $u=C'_{6,3}$ and $f=C'_{3,3}$ ?
Why order of elements is so important ? The problem doesn't say anything about
the order of the even numbers !
Thank you.
Best Answer
Using combinations means you are choosing a certain number from a set, where order does not matter.
As for this problem, order does matter. $(2,4,6)$ and $(4,2,6)$ are different possibilities, therefore you should use permutations.