Getting a "straight" in dice rolls Suppose that you have $k$ dice, each with $N$ sides, where $k\geq N$.  The definition of a straight is when all $k$ dice are rolled, there is at least one die revealing each number from $1$ to $N$.  
Given the pair $(k,N)$, what is the probability that any particular roll will give a straight?

What about simply $\dfrac{^k\text{P}_n(k-n)!}{n^k}$, since $k \ge n$. If $k=n$ then we simply get $\dfrac{n!}{n^k}$?
Since there are only $n$ sides to the dice and if $k=n$, we are asking the total number of permutations of $n$ different values which is $^n\text{P}_n=n!$ divided by all the possible outcomes of $n^k$. If $k>n$ we just replace $^n\text{P}_n$ with $^k\text{P}_n$ assume some values besides $n$ different possible sides are included thus multiplying the total possible outcomes with at least a straight.
