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Counting 6 digit numbers with conditions

Source: (Indian) RMO 2008 Problem 4

November 9, 2008
combinatorics unsolvedcombinatoricsRMO

Problem Statement

Find the number of all 6 6-digit natural numbers such that the sum of their digits is 10 10 and each of the digits 0,1,2,3 0,1,2,3 occurs at least once in them. [14 points out of 100 for the 6 problems]
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