# math logic

posted by
**M.A.**
.

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?

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?