Permutations

Side Topic:

If you have $k$ selections, with replacement, from a set of $n$ distinct objects (E.G. 6 sides of a die), then the size of the Sample Space is $n^k$. So the total amount of possible outcomes for rolling a dice 3 times is $6^3$. (Technically if you get a side of the die, you replace it again for the next roll).

Permutations: That, but without replacement.

Formal Definition:

Any ordered sequence of $k$ objects taken without replacement from a set of $n$ distinct objects is called a permutation of size $k$ of the objects. The number of permutations of size $k$ that can be constructed from the $n$ objects is denoted by ${}_n{P}_k$.

${}_n{P}_k=n(n-1)(n-2)...(n-k+2)(n-k+1)$ OR
${}_n{P}_k=\frac{n!}{(n-k)!}$

Note: The order of which you’re dealt matters, making Permutations grow so quickly. So, in dice, a $1,4,2,5$ and a $1,2,4,5$ are different.