Problem 43575. Probabilities - More brains than luck

This problem is related to Problem 596. More luck than brains where the test suite checks 3 times if the outcome of the solution is a random number between 1 and 6.

Using brain, the "solver" would be interested in computing the probability of passing a general test (with some other interesting probabilities) where the suite checks C times if the outcome of the solution is a random number between 1 and N.

So, here is the problem:

1. Each test in the suite checks if a random number between 1 and N is guessed.
2. There are C tests in the suite.

Output these values, given inputs N,C,K:

1. P = the probability of passing the test suite.
2. XK = the probability that the number of times the function must be run to get a success (passing the test suite) is K.
3. M = the mean number of times the function must be run to get a success.

You will see that, for N=6 and C=3, then M=216.