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partition 15 people into 6 groups of 3, 3, 3, 2, 2, and 2

Source: 2008 Indonesia TST stage 2 test 2 p4

December 14, 2020
probabilitypartitioncombinatorics

Problem Statement

There are 1515 people, including Petruk, Gareng, and Bagong, which will be partitioned into 66 groups, randomly, that consists of 3,3,3,2,23, 3, 3, 2, 2, and 22 people (orders are ignored). Determine the probability that Petruk, Gareng, and Bagong are in a group.
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