Question

4. Marta has brought n distinct doughnuts for her three friends. She wants each doughnut to be tried by at least one person. She can give a complete doughnut to each friend, But they can also be split into two halfs. However, they are too small to split into three pieces. She will not eat any doughnuts herself . Given this, how many ways can the doughnuts be distributed?

Answer 1

For each do-nut, it can either be given to exactly one of the 3 friends in 3 ways OR it can be split can given to 3 different friends in ways

Total options for each donut are

As there are donuts, and the way in which one donut is given for tasting is independent of the rest, we have different ways of distributing the donuts for trying by Marta's friends

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