# Problem I. 118. (December 2005)

**I. 118.** We have *n* ceramic piggy banks and *n* keys, each corresponding to exactly one of the banks. We throw one key into each bank at random. Then we break open *t* ceramic pigs. Find the probability that we are able to open the remaining banks using the keys found in the broken ones without any further breaking. Write a program that estimates this probability by making *k* experiments. If *n*<10, then we should also compute the exact probability by examining all possible cases.

Your program should read the values of *n*, *t* and *k* from the keyboard, then make the experiments and display the resulting relative frequencies (that is, the ratio of successful outcomes to *k*), further, the exact probability.

The source code of the program should be submitted (`i118.pas`, `i118.cpp`, ...).

(10 pont)

**Deadline expired on January 16, 2006.**

### Statistics:

14 students sent a solution. 10 points: Balambér Dávid, Czigler András, Gombos Gergely, Kiss Dániel Miklós, Véges Márton. 6 points: 2 students. 4 points: 4 students. 0 point: 3 students.

Problems in Information Technology of KöMaL, December 2005