Partitions into groups - Exercise set 1

This exercise set contains some solved exercises on partitions into groups. The theory needed to solve these exercises is introduced in the lecture entitled Partitions into groups.

Exercise 1.1

John has a basket of fruit containing one apple, one banana, one orange and one kiwi. He wants to give one fruit to each of his two little sisters and two fruits to his big brother. In how many different ways can he do this?

Solution

Exercise 1.2

Ten friends want to play basketball. They need to divide into two teams of five players. In how many different ways can they do this?

Solution