A hint to get started
Partition children into unlabelled groups
In how many ways can a party of 10 children be divided into
(i) one group of 2 and one group of 8,
(ii) two groups of 5,
(iii) three groups of sizes 2,4 and 4?
CJC · Lecture · Example 10
Decide whether order matters and repetition is allowed; then count stages or disjoint cases.