math logic

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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
----------------------
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?

  • math logic -

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

    You are right.

  • math logic -

    Thank you!

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