Question

I have four identical oranges. How many ways are there for me to divide these oranges into at most three groups?

Answer 1

"At most" connotes 1, 2 or 3 groups

For one group = one way....all of them together

For two groups.....2 + 2 or 3 + 1 = two ways ...{the oranges are indistinguishable, so 1 + 3 is the same grouping as 3 + 1 }

For 3 groups = 1 + 1 + 2 = one way {again, they are indistinguishable}

So ….. four ways.....

Explanation: