Drawing Pebbles

A secret box holds $N$ pebbles. Each pebble has one of the colors numbered $1$ through $M$.

You draw $K$ pebbles at random from the box. Write a program that computes the probability that every drawn pebble has the same color. Every choice of $K$ distinct pebbles is equally likely.

The first line contains the number of colors $M$ ($1 \le M \le 50$).

The second line contains $M$ integers, the pebble count of color $1$ through color $M$ in that order. Each value is at least $1$ and at most $50$. The total number of pebbles $N$ is the sum of these $M$ values.

The third line contains $K$ ($1 \le K \le N$).

Print the probability that every drawn pebble has the same color, rounded half up at the 11th digit after the decimal point and shown to the 10th digit. Always print exactly 10 digits after the decimal point. A probability of $1$ is printed as 1.0000000000.