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For a gaming competition, 8 girls are planning on splitting up into 3 (non-empty) groups. How many ways can they split up into these groups?(a) 465(b) 1056(c) 966(d) 3215I have been asked this question in unit test.My query is from Counting in division Counting of Discrete Mathematics

Answer»

The correct choice is (c) 966

For explanation I would say: Using the inclusion-exclusion principle, the total number of WAYS of SPLITTING the GIRLS into 3 groups is 3^8 + 3.(2^8) + 3.(1^8). However, SINCE the three groups are identical we need to DIVIDE by 3!. Hence, the answer is 966.



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