Probability of getting 6 k times in a row What is the probability of getting $6$ $K$ times in a row when rolling a dice N times?
I thought it's $(1/6)^k*(5/6)^{n-k}$ and that times $N-K+1$ since there are $N-K+1$ ways to place an array of consecutive elements to $N$ places.

So, let's say that X is a random variable for tracing the number of 6s.
Let's say that C is the condition for the 6s to be consecutive.
Since the task is to find the probability of gaining at least K subsequent 6s, we can look for probability of event A-at least K subsequent 6s fell this way:
     P(A)=P(X=K|C)+P(X=K+1|C)+...+P(X=K+N|C)+...,
where P(X=K|C) is the probability of K 6s falling under the condition that they are consecutive.
Since the event that K 6s have fallen is independent from the event that all the 6s are in order, we can say that:
    P(X=K|C)=P(X=K)*P(C).
Is this the right way to go?
Edit:
Doesn't seem right because the events ARE independent, because K 6s need to fall in order for them to be consecutive.
