Problem #PRU-66056

Problems Probability and statistics Probability theory Discrete distribution Discrete Mathematics Set theory and logic Set theory Inclusion-exclusion principle Algebra Sequences Recurrent relations Recurrent relations (other)

Problem

An incredible legend says that one day Stirling was considering the numbers of Stirling of the second kind. During his thoughtfulness, he threw 10 regular dice on the table. After the next throw, he suddenly noticed that in the dropped combination of points there were all of the numbers from 1 to 6. Immediately Stirling reflected: what is the probability of such an event? What is the probability that when throwing 10 dice each number of points from 1 to 6 will drop out on at least one die?