A group of five students needs to break into two smaller groups in order to tackle the two different assignments associated with a larger group project. Naturally, they feel that it would be most fair to break into groups of two and three. How many ways are there to do this?

Question

Choose one:
5
10
20
40
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My reasoning:
There are 5 students. I will name them student A, B, C, D, and E.
First grouping: AB
CDE
BC
DEA
etc. = 5 ways to combine students.

Second grouping: AC
BDE
BD
EAC
etc. = 5 ways to combine students.

Third grouping: CE
ABD
etc. = 5 ways to combine students.

Fourth grouping: AD
etc. = 5 ways

Fifth grouping: AE
etc. = 5 ways

5 groupings with 5 ways to combine students = 20 ways to group.

So, is the answer "20" or am I to assume
that they can be further grouped depending upon the unexplained tasks of
the class project?

Answer 1

Using combinations,
number of ways = C(5,3)xC(2,2) = 20x1 = 20

You are right.

Answer 2

Thank you!