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Probability in lottery

Source: Finnish Mathematics Competition 2001, Final Round, Problem 4

November 14, 2011
probabilitycombinatorics unsolvedcombinatorics

Problem Statement

A sequence of seven digits is randomly chosen in a weekly lottery. Every digit can be any of the digits 0,1,2,3,4,5,6,7,8,9.0, 1, 2, 3, 4, 5, 6, 7, 8, 9. What is the probability of having at most fi ve diff erent digits in the sequence?
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