Question

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) 3215

I have been asked this question in unit test.

My query is from Counting in division Counting of Discrete Mathematics

Answer 1

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.