Which Groupings Are Right?

Difficulty: Hard · Topics: Discrete Mathematics, Combinatorics, Combinations

Which of the following statements are true?

I. A team of 6 can be split into three groups of two in 15 different ways.

II. A team of 5 can be split into a group of 2 and a group of 3, one going to Samarkand and the other to Bukhara, in 20 different ways.

III. A team of 5 can be split into three groups of two, two and one people in 30 different ways.